
    CABLE/HOME COMMUNICATION CORPORATION, M/A-Com, Inc., Home Box Office, Inc., and Showtime/The Movie Channel, Inc., Plaintiffs-Appellees, v. NETWORK PRODUCTIONS, INC. and Shaun Kenny, Defendants-Appellants. Bob Cooper, Jr., et al., Defendants.
    Nos. 88-5647, 89-5081.
    United States Court of Appeals, Eleventh Circuit.
    June 4, 1990.
    
      Lisa Bennett, Coral Gables, Fla., for defendants-appellants.
    Lawrence G.D. Scarborough, Alan H. Blankenheimer, Phoenix, Ariz., for plaintiffs-appellees.
    Before FAY and KRAVITCH, Circuit Judges, and THOMPSON , District Judge.
    
      
       Honorable Myron H. Thompson, U.S. District Judge for the Middle District of Alabama, sitting by designation.
    
   FAY, Circuit Judge:

This consolidated appeal presents the recurring problem of piracy of satellite television programming. Defendants-appellants helped to create, promote, distribute and import for financial gain various pirate, computer software chips and devices, which enabled display of plaintiffs-appel-lees’ programming intended for their paying subscribers by disrupting the functioning of their copyrighted computer program designed to scramble satellite transmissions. Plaintiffs-appellees brought this action alleging violations of the copyright and communications laws. The district court granted summary judgment to plaintiffs-appellees and awarded them statutory damages and their requested attorneys’ fees. In addition to appealing these rulings, defendants-appellants also appeal the district court’s denial of their motion to dismiss for lack of personal jurisdiction and denial of their motion for extended time to respond to the summary judgment motion. After thorough review of the record, we affirm.

I. FACTUAL BACKGROUND

A. The Programmers

Plaintiffs-appellees Home Box Office, Inc. (HBO) and Showtime/The Movie Channel, Inc. (Showtime) provide pay television programming through electromagnetic signals via a communications satellite to subscription television services, such as cable television systems, and to individual subscribers. In order to prevent individuals who have not subscribed to their service from viewing their programming, HBO and Showtime use the VideoCipher®II system to scramble or encrypt the audio and video portions of their satellite transmissions. Subscribers with satellite dish antennas use the VideoCipher®II to decode programming for which they have paid. Upon a customer’s payment of the subscription fee, the program providers cause the subscriber’s VideoCipher®II to descramble their programming.

The core of the VideoCipher®II decryption technology is a computer program, Control Microprocessor Software (CMS), which is stored in a key integrated circuit, the U-30 chip, in the VideoCipher® II de-scrambler module. Plaintiff-appellee M/A-COM, Inc. (M/A-COM) is the owner of two versions of the CMS computer program work registered with the United States Copyright Office under numbers TX1-952-652, dated December 18, 1986, and TX1-971-759, dated January 27, 1987. The copyright notice is affixed to the chassis of the VideoCipher®II descrambler or to the integrated circuit board on which the U-30 chip is located, and a copyright notice is embedded in the CMS program itself. M/A-COM has authorized as its licensee plaintiff-appellee Cable/Home Communication Corporation (Cable/Home), a wholly owned subsidiary of plaintiff-appellee General Instrument Corporation. Cable/Home sells the VideoCipher®II in Florida and elsewhere, with annual sales generating approximately $100,000,000.00.

B. The Pirates and Their Chips

Defendant-appellant Shaun Kenny is the president, sole director and shareholder of defendant-appellant Network Productions, Inc. (Network), a video producer. In addition to making video tapes for such uses as corporate seminars and legal depositions, Network produces a weekly news program, known as Boresight News (Boresight). This program, transmitted by satellite to the United States, Canada, Mexico and the Caribbean islands, presents industry news to satellite dish dealers, distributors and private owners. Producer Kenny has marketed Boresight as a consumer-oriented news program and has utilized the show to comment upon and to criticize the practices and products of programmers.

Following the advent of scrambling signals by programmers, Kenny decided that scrambled programming was not being offered to home satellite dish owners at a reasonable price competitive with those offered to cable television subscribers. He commenced an informative consumer campaign, which included discussion on Bore-sight as well as sales of devices designed to break or defeat the programmers’ methods of scrambling signals. His alleged purposes in providing such information have been to instigate legislation protecting competition in the marketplace by insuring programming to consumers at a fair price and to show viewers that the VideoCipher®II is compromised easily and, therefore, is a poor investment.

Integrated circuit chips, designed to replace the U-30 chip in the VideoCipher®II and to alter the functioning of the VideoCi-pher®II enabling a user to descramble encrypted pay television programming, are generally and collectively referred to as pirate chips. Two methods have been employed to utilize pirate chips: the “Three Musketeers” technique, whereby subscription to a single programming service, usually the least expensive, is used to access all other programming services without further payment or authorization, and “cloning,” whereby multiple units are altered and linked so that any one unit subscribing to pay programming acts as the conduit for receipt of such services by all the units without additional payment or authorization. Kenny has testified that “[u]sing a pirate chip is totally illegal if you’re receiving programming you’re not paying for.” With knowledge of the potential legal consequences, Kenny pursued his publicity and sale of pirate chips.

Kenny had another business known as Bag-O-Parts, which sold a kit used to decode the VideoCipher®II by allowing users to unscramble video portions of scrambled transmissions to which they did not subscribe. During 1986, Bag-O-Parts not only was Kenny’s sole source of income, but also supported Boresight for a time. Kenny profited $17,000.00 from sales of Bag-O-Parts.

Kenny advertised and promoted his Bag-O-Parts business on Boresight as well as the Dealer Demo chip, which also unscrambled the video transmissions of the Video-Cipher®II. This device, designed for dealers’ showroom display, simultaneously overlays the middle of the screen with a solid black box, which allows insertion of a message. The Dealer Demo chip is an 86% copy of the CMS program of YideoCi-pher®II and contains a copy of the M/A-COM copyright notice.

Kenny also publicized on Boresight a small plastic socket for insertion into the slot containing the U-30 chip to allow easy removal and insertion of the U-30 chip. Additionally, the socket “facilitates the ... the person to install a pirate chip” in place of the U-30 chip. Because the process of inserting the socket into the VideoCi-pher®II involved soldering, a procedure some individuals are unqualified to perform, Kenny offered the service of removing the U-30 chip and installing the socket for customers who sent their VideoCi-pher®II circuitry boards to him for the procedure. Kenny advertised this service for $39.00 per unit, payable to cash. He boasted that this was another “way for Shaun to make money during all this,” and even offered to remove the pirate chip and socket and to replace the U-30 chip if customers ever had to return their circuitry boards to M/A-COM because Kenny was “sneaky.”

While these descrambling methods for video reception were profitable, Kenny recognized that the ability to unscramble both audio and video would be more valuable. Kenny and former defendant Bob Cooper, Jr., a commentator on Boresight and publisher of Coop Satellite Digest, a publication similar in information and commentary to Boresight, became interested in a method to “break the VCII.” In approximately May, 1986, Kenny learned of the formation of DESUG (Data Encryption Standard Users Group), a group composed of individuals committed to breaking the VideoCi-pher®II as an academic exercise. Through Boresight, Kenny collected funds and equipment for DESUG to enable the group to conduct their research. Kenny sent $1,250.00 to DESUG member and former defendant Stephen Bepko, who purchased a VideoCipher®II and devised pirate chips for compromising M/A-COM’s VideoCipher® II. Bepko developed the Rabbit Writer and the Rabbit Video chips, respectively 94% and 98% copies of the CMS program within the U-30 chip, and used as his marketing name, Rabbit Trading Company.

DESUG member and former defendant William Ward requested money from Kenny for a computer and burner in order to make pirate chips to compromise the Video-Cipher®II system. Kenny ultimately sent Ward $900.00 with which Ward made a Three Musketeers chip, a 93% copy of the CMS program of the U-30 chip, to compromise the VideoCipher®II. Ward marketed this chip under the name Comtech, Ltd. When Kenny learned that Ward intended to reduce the price on his pirate chip, Kenny informed Ward that he could not advertise his product on Boresight. Ward inferred that Kenny would denigrate his pirate chip on Boresight and interpreted Kenny’s admonition as a definite “commercial threat.”

In addition to publicizing and financially assisting the production of pirate chips on Boresight, Kenny also demonstrated the use of pirate chips on the show. On the December 4, 1986 show, for example, Kenny, Cooper and former defendant Karen Howes, a reporter and journalist on Bore-sight, discussed and demonstrated three pirate chips, two of the Three Musketeers type and one clone, which enabled the user also to receive the audio transmission on the VideoCipher®II. Kenny actually demonstrated with a VideoCipher®II the “minor surgery” necessary for inserting a pirate chip and advised his audience to tape that segment of Boresight for future use. Kenny announced on Boresight the availability of pirate chips to break the VideoCi-pher®II and acknowledged the profit in these chips:

Well are you ready? Is the industry ready? Is [sic] M/A-COM ready? Is cable ready? Is programmers ready? Are they all ready? And most, most importantly is the Motion Picture Association ready for this? Because what this is ... is a broken VC-II, and no longer is it a requirement for you to pay for services that you feel are over-priced. Unfortunately, you’re still gonna have to pay the $400 for the decoder and you’re gonna make some people rich by paying $250 to $400 for a system that breaks the VC-II, but that’s the price you gotta pay if you want to cheat in the world.

Boresight News Transcript at 9-10 (Dec. 4, 1986). R8-80-Ex.D-9-10.

Kenny ultimately publicized and endorsed on Boresight two Three Musketeers chips, X-ACT and Integrated Digital Systems or IDS, manufactured by separate Canadian companies. On Boresight, Cooper warned the audience that pirate chips should be purchased from companies outside the United States “[bjecause it’s plainly illegal to be dealing in this sort of device from within the United States.” Viewers of Boresight were informed repeatedly of the illegality of pirate chips. With concern over impending lawsuits, Kenny used Boresight to request contributions from viewers for a legal defense fund. Therefore, not only were Kenny and the other former defendants aware of the unlawful sale and use of pirate chips, but also the Boresight audience, potential purchasers and users of pirate chips, were so informed.

C. The Descrambling Summit

Kenny used Boresight to promote attendance at a Descrambling Summit, held in three successive sessions from January 14 through 22, 1987, on the Islands of Provi-denciales, Turks and Caicos in the British West Indies. Cooper, who maintained an office in Fort Lauderdale, Florida, organized the summit. The purpose of the summit was to educate those attending on the descrambling system, including how the Vi-deoCipher® II had been broken, and the availability of various pirate chips. Each of the three hundred attendees paid a fee of $1,500.00, which included round-trip air fare from Fort Lauderdale to the island of Providenciales through a Fort Lauderdale travel agency, all accommodations, and four descrambling or pirate chips with an advertised street value of $1,400.00. Additionally, Boresight viewers were informed that they would be instructed at the summit on treating the descrambler business as a “profit center” or “how to make money with the chips.” Cooper paid Kenny $14,500.00 to videotape the entire summit. The videotapes were to be sold for $195.00 each, and Kenny and Cooper planned to divide the profits.

On the first day of the summit, Cooper explained to the attendees that the summit was being held outside the United States in order to avoid prohibitive American laws. Interestingly, a portion of the summit program was devoted to education in American copyright and communications laws by a Canadian attorney. He instructed that, under American statutory and case law, anyone manufacturing, distributing, selling or installing equipment enabling a party to intercept encoded transmissions could be subject to civil or criminal penalties. He advised that “it will be very difficult to obtain any financial gain through exploitation of this technology without risking some potentially serious consequences.”

Regarding American copyright laws, the attorney explained that the basis for a copyright violation in descrambling encoded transmissions is the unauthorized use of the programming for which the programmer holds the copyright. He further reported that “[tjhose who claim to have extracted the software from the memory chips inside of VideoCipher® acknowledge finding copyright notices contained in the data.” He advised the summit attendees that breaking the VideoCipher® II and watching a copyrighted program without paying for it violated the programmer’s copyright.

Furthermore, Cooper informed the summit audience of a lawsuit filed January 7, 1987, in federal district court in Arizona by plaintiffs-appellees Cable/Home, M/A-COM and HBO against individuals and their respective companies through which they did business for unauthorized de-scrambling of VideoCipher®II transmissions. He advised that the suit sought to prevent the defendants from manufacturing or selling decoding devices, to recover the defendants’ profits from their unlawful sales and to award the plaintiffs monetary damages for the alleged violations of the copyright and communications laws. He also told the attendees that a spokesman for Cable/Home had admonished that the Arizona civil suit was the first action in a concerted effort by Cable/Home to stop piracy in satellite television.

Despite the legal instruction given at the Descrambling Summit and the knowledge of a lawsuit filed for the use of decoding devices, the attendees received their promised pirate chips on the last day of the summit. They were given the option of taking the pirate chips with them or having the pirate chips mailed to them in the United States. Cooper instructed those electing to take their pirate chips with them on completion of their customs declaration, and told them that the pirate chips had not been purchased. He assured these individuals that, if their pirate chips were confiscated, then he would replace them. The United States Customs Service seized pirate chip's in the possession of those who had attended the second session of the De-scrambling Summit and returned to the United States on January 19, 1987.

D. Prior Procedure

Upon learning of the Descrambling Summit, where pirate chips were distributed and sold, plaintiffs filed their original complaint in the Southern District of Florida, seeking, among other requests, a preliminary and permanent injunction, statutory damages, attorneys’ fees and costs. Defendants filed motions to dismiss on several grounds, including lack of personal jurisdiction over them in Florida. The district court denied these motions to dismiss in an omnibus order.

On June 17, 1987, the district court entered a preliminary injunction generally enjoining defendants from manufacturing, installing, marketing, using, importing, and distributing any device capable of assisting in the unauthorized interception of transmission signals carrying pay programming by compromising the copyrighted CMS program within the U-30 chip. Furthermore, defendants were prevented from destroying or concealing any records regarding transactions and profits resulting from defendants’ involvement with such intercepting devices. Despite the preliminary injunction, Kenny continued to promote pirate chips to his viewing audiences, including availability from a Mexican company.

In answering the second amended and controlling complaint, basing jurisdiction on 28 U.S.C. sections 1331 and 1338, defendants asserted the affirmative defense of First Amendment protection for information regarding pirate chips that they had disseminated. Alleging defendants’ willful violation of the copyright and communications laws, plaintiffs moved for summary judgment. The district court granted plaintiffs’ unopposed motion for summary judgment by default against defendants, and denied the motion for extension of time to respond to plaintiffs’ summary judgment motion by defendants Kenny and Network because of their repeated failure to comply with the terms of the court and the local rules. Defendant Cooper did not oppose entry of summary judgment against him.

Defendants Network and Kenny moved to vacate or amend the judgment entered against them pursuant to Rule 59(e) of the Federal Rules of Civil Procedure. Admittedly, their motion was made outside of ten days after entry of judgment as required by Rule 59(e). Defendants, however, explained that they recently had acquired new counsel, who had not had sufficient time to oppose plaintiffs’ summary judgment motion. The district court entered an order giving defendants’ new counsel ten days, with no extensions, to respond to plaintiffs’ summary judgment motion on the merits. Nevertheless, defendants’ new counsel moved for an additional ten days to respond to plaintiffs’ summary judgment motion. The district court denied this motion for a second extension of response time.

Defendants Network and Kenny filed their opposition to plaintiffs’ summary judgment motion within the first extension of time granted to them by the district court. Among their grounds for opposition, defendants claimed that they were protected by the First Amendment and their warnings of illegality. Upon consideration of defendants’ opposition, the district court denied defendants’ motion to vacate or amend its previous entry of summary judgment.

Following the district court’s confirmation of summary judgment for plaintiffs, they applied for joint and several assessment of attorneys’ fees and costs. Since they had elected statutory damages because of their inability to obtain profit information from defendants, plaintiffs also moved for reconsideration of trying the issues of damages and attorneys’ fees. Because statutory damages, attorneys’ fees and the scope of the permanent injunction, the remaining issues in the case, were committed by statute to the district court’s discretion, plaintiffs contended that a trial was not warranted.

The district court held a status conference on all pending motions, wherein plaintiffs requested maximum statutory damages. On June 27, 1988, the district court issued final judgment and a permanent injunction, which reiterated the original preliminary injunction. The court also vacated its order setting trial, and awarded plaintiffs joint and several statutory damages with interest against defendants Network, Kenny and Cooper in the amount of $20,-000.00 for their willful, direct and contributory copyright infringements and their for-profit violations of the communications laws, with additional damages and interest against Network and Kenny for separate willful, for-profit violations of the communications laws. Referring plaintiffs’ request for attorneys’ fees and costs to the magistrate for determination, the district court retained jurisdiction over these issues pending resolution.

Following a hearing, including expert testimony, review of the record, and weighing precedential guidelines for awarding attorneys’ fees, the magistrate recommended granting plaintiffs’ requested attorneys’ fees and costs in the amount of $451,789.06. The magistrate acknowledged that plaintiffs’ successful litigation strategy was for the purpose of protecting their copyrighted asset. They sought not only to enjoin the conduct of these defendants, but also to deter others in future attempts to compromise the VideoCi-pher®II for profit. After reviewing the magistrate’s order as well as responses thereto by defendants and plaintiffs, the district court’s final judgment affirmed and adopted the magistrate’s report and recommendation of attorneys’ fees and costs in the amount of $451,789.06.

From these proceedings, defendants-appellants Network and Kenny have appealed five issues to this court. First, they contend that the district court erred in entering summary judgment against them. Second, defendants-appellants argue that they were entitled to a jury or bench trial regarding damages. Third, they claim that the district court abused its discretion by awarding excessive attorneys’ fees to plaintiffs. Fourth, they fault the district court for denying their motion to dismiss on the ground that the court lacked personal jurisdiction over the defendants in Florida. Fifth, Network and Kenny assert that the district court abused its discretion in denying defendants’ motion for additional time within which to respond to the motion for summary judgment. We will address these appellate issues seriatim.

II. ANALYSIS

A. The Grant of Summary Judgment to Plaintiffs

Summary judgment is appropriate “if the pleadings, depositions, answers to interrogatories, and admissions on file, together with the affidavits, if any, show that there is no genuine issue as to any material fact and that the moving party is entitled to a judgment as a matter of law.” Fed.R. Civ.P. 56(c). The Supreme Court has specified procedural and substantive standards for deciding when summary judgment is proper. Celotex Corp. v. Catrett, 477 U.S. 317, 106 S.Ct. 2548, 91 L.Ed.2d 265 (1986); Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986). The movant “bears the initial responsibility of informing the district court of the basis for its motion” by identifying those portions of the record that demonstrate the absence of genuine issues of material fact. Celotex, 477 U.S. at 323, 106 S.Ct. at 2553. When a motion for summary judgment has been made properly, the burden of production shifts to the nonmoving party “to go beyond the pleadings and by her own affidavits, or by the ‘depositions, answers to interrogatories, and admissions on file,’ designate ‘specific facts showing that there is a genuine issue for trial.’ ” Celotex, 477 U.S. at 324, 106 S.Ct. at 2553 (quoting Fed.R.Civ.P. 56(e, e)).

Anderson explains how the district court should evaluate the evidence submitted with a summary judgment motion. Analogizing a summary judgment decision with directed verdict analysis, the Court defined a factual dispute as genuine “if the evidence is such that a reasonable jury could return a verdict for the nonmoving party.” Anderson, 477 U.S. at 248, 106 S.Ct. at 2510; see Everett v. Napper, 833 F.2d 1507, 1510 (11th Cir.1987); Dominick v. Dixie Nat’l Life Ins. Co., 809 F.2d 1559, 1572 (11th Cir.1987). Clarifying the definition of a genuine factual dispute preventing summary judgment under Rule 56(c), the Court explained: “By its very terms, this standard provides that the mere existence of some alleged factual dispute between the parties will not defeat an otherwise properly supported motion for summary judgment; the requirement is that there be no genuine issue of material fact.” Anderson, 477 U.S. at 247-48, 106 S.Ct. at 2510 (emphasis in original). Furthermore, the Court instructed that “the substantive law will identify which facts are material” and that the trial judge “must view the evidence presented through the prism of the substantive evidentiary burden” in ruling on a summary judgment motion. Anderson, 477 U.S. at 248, 254, 106 S.Ct. at 2510, 2513.

Appellate review of a grant of summary judgment is plenary, and we must apply the same legal standards used by the district court. Livernois v. Medical Disposables, Inc., 837 F.2d 1018, 1021-22 (11th Cir.1988); Carlin Communication, Inc. v. Southern Bell Tel. & Tel. Co., 802 F.2d 1352, 1356 (11th Cir.1986). This court has reviewed thoroughly the ample record in the case, and we have found that the undisputed, operative facts concerning the open promotion and sale of pirate chips by defendants for financial gain, even when viewed most favorably as to defendants, as well as reasonable inferences drawn therefrom do not create a genuine issue of material fact warranting trial. See Augusta Iron & Steel Works, Inc. v. Employers Ins. of Wausau, 835 F.2d 855, 856 (11th Cir.1988) (per curiam); Carlin Communication, 802 F.2d at 1356; Warrior Tombigbee Transp. Co. v. M/V Nan Fung, 695 F.2d 1294, 1296-97 (11th Cir.1983). Therefore, the copyright and communications claims must be analyzed under the controlling substantive law in order to determine if the district court’s decision was correct as a matter of law. Everett, 833 F.2d at 1510; see Fed.R.Civ.P. 56(c).

1. Copyright Violations

The Copyright Act of 1976 (Copyright Act), 17 U.S.C. § 101 et seq., is the congressional implementation of an affirmative constitutional duty under the copyright and patent clause “[t]o promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.” U.S. Const, art. I, § 8, cl. 8; Dallas Cowboys Cheerleaders, Inc. v. Scoreboard Posters, Inc., 600 F.2d 1184, 1187 (5th Cir.1979); see Sony Corp. v. Universal City Studios, Inc., 464 U.S. 417, 428-29, 104 S.Ct. 774, 782, 78 L.Ed.2d 574 (1984); Mazer v. Stein, 347 U.S. 201, 219, 74 S.Ct. 460, 471, 98 L.Ed. 630 (1954); Washingtonian Publishing Co. v. Pearson, 306 U.S. 30, 36, 59 S.Ct. 397, 400, 83 L.Ed. 470 (1939). The Copyright Act provides a fair return to authors and inventors by protecting their works from exploitation by others. See Harper & Row, Publishers, Inc. v. Nation Enterprises, 471 U.S. 539, 546, 105 S.Ct. 2218, 2223, 85 L.Ed.2d 588 (1985); Twentieth Century Music Corp. v. Aiken, 422 U.S. 151, 156, 95 S.Ct. 2040, 2043-44, 45 L.Ed.2d 84 (1975). The district court issued its final judgment and permanent injunction based on defendants’ willful, direct and contributory copyright infringements. Accordingly, we must examine the substantive law of direct and contributory copyright infringement in order to determine if defendants’ acts violated plaintiffs’ copyrighted CMS computer program, stored in the U-30 chip.

a. Direct Copyright Infringement

The Copyright Act extends protection to computer programs. 17 U.S.C. §§ 101, 102(a) (1982); Apple Computer, Inc. v. Formula Int’l Inc., 725 F.2d 521, 524 (9th Cir.1984); Williams Electronics, Inc. v. Artic Int’l, Inc., 685 F.2d 870, 875 (3d Cir.1982). The seminal case of Baker v. Selden, 101 U.S. 99, 25 L.Ed. 841 (1879), requires federal courts to distinguish between unprotected ideas and protected expression, a concept which has been incorporated in the Copyright Act. See Harper & Row, 471 U.S. at 556, 105 S.Ct. at 2228; Miller v. Universal City Studios, Inc., 650 F.2d 1365, 1368 (5th Cir. July 1981); see also Mazer, 347 U.S. at 217, 74 S.Ct. at 470 (“Unlike a patent, a copyright gives no exclusive right to the art disclosed; protection is given only to the expression of the idea — not the idea itself.” (citation omitted)). Courts have struggled with this dichotomy in the context of computer programs, given the various types and functions of these programs. See, e.g., Whelan Assocs., Inc. v. Jaslow Dental Laboratory, Inc., 797 F.2d 1222, 1236-40 (3d Cir.1986), cert. denied, 479 U.S. 1031, 107 S.Ct. 877, 93 L.Ed.2d 831 (1987); Formula, 725 F.2d at 523-25; Apple Computer, Inc. v. Franklin Computer Corp., 714 F.2d 1240, 1252-54 (3d Cir.1983), cert. dismissed, 464 U.S. 1033, 104 S.Ct. 690, 79 L.Ed.2d 158 (1984). We find persuasive and applicable in this case the reasoning of the Third Circuit in Franklin, analyzing not only the copyrightability of a program embedded on a ROM (Read Only Memory) or semi-conductor chip inserted into the circuitry of a computer, but also the copyright protection for a program communicating with the operating system of a computer as opposed to the user. Franklin, 714 F.2d at 1249-54; see also Formula, 725 F.2d at 525 (“The computer program when written embodies expression; never has the Copyright Act required that the expression be communicated to a particular audience.”); Tennessee Fabricating Co. v. Moultrie Mfg. Co., 421 F.2d 279, 281 (5th Cir.) (“[L]ack of artistic merit is no bar to copyright.”), cert. denied, 398 U.S. 928, 90 S.Ct. 1819, 26 L.Ed.2d 91 (1970).

Defendants-appellants’ direct copyright infringement relates to the use, demonstration, promotion, and sale by Kenny through Network of the Dealer Demo chip, an 86% copy of the CMS program within the U-30 chip of the VideoCipher®II. Public distribution of a copyrighted work is a right reserved to the copyright owner, and usurpation of that right constitutes infringement. 17 U.S.C. § 106(3); 2 Nimmer on Copyright § 8.11[A] (1988). Because Kenny demonstrated and promoted the Dealer Demo chip on Boresight, there is irrefutable evidence of direct copyright infringement in this case.

Defendants-appellants have claimed that their affirmative defense of fair use precludes a finding of copyright infringement. “Fair use” describes “limited and useful forms of copying and distribution that are tolerated as exceptions to copyright protection.” Pacific & Southern Co. v. Duncan, 744 F.2d 1490, 1494 (11th Cir.1984), cert. denied, 471 U.S. 1004, 105 S.Ct. 1867, 85 L.Ed.2d 161 (1985); see also Tennessee Fabricating, 421 F.2d at 284 (“[T]o constitute ‘fair use’ the permitted use must be for some legitimate, fair and reasonable purpose.”)- The Copyright Act mandates four nonexclusive factors which courts shall consider case by case in determining fair use, a mixed question of fact and law:

[T]he fair use of a copyrighted work, including such use by reproduction in copies ... for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright. In determining whether the use made of a work in any particular case is a fair use the factors to be considered shall include—
(1) the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
(2) the nature of the copyrighted work;
(3) the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
(4) the effect of the use upon the potential market for or value of the copyrighted work.

17 U.S.C. § 107 (1982); Harper & Row, 471 U.S. at 549, 560-61, 105 S.Ct. at 2225, 2230-31; Duncan, 744 F.2d at 1494-95 & n. 8. With respect to the first factor, the Supreme Court has clarified that “a commercial or profit-making purpose” is presumptively unfair. Sony, 464 U.S. at 448-49, 104 S.Ct. at 792; Harper & Row, 471 U.S. at 562, 105 S.Ct. at 2231; Duncan, 744 F.2d at 1496. Implicit in this presumption is some meaningful likelihood that future market harm exists. Sony, 464 U.S. at 451, 104 S.Ct. at 793. “The crux of the profit/nonprofit distinction is not whether the sole motive of the use is monetary gain but whether the user stands to profit from exploitation of the copyrighted material without paying the customary price.” Harper & Row, 471 U.S. at 562, 105 S.Ct. at 2231. Not only did Kenny have a commercial purpose, evidenced by his own statements on Boresight, but also he utilized the show to encourage others to make a profit by selling pirate chips, complete with demonstrations of how to descramble programming on the VideoCipher®II using pirate chips. Kenny’s flagrant commercial purpose whereby he exploited the subject CMS computer program cannot be disguised as fair use.

The second factor that we must consider is the nature of the copyrighted work. This factor is “highly relevant to whether a given use is fair.” Harper & Row, 471 U.S. at 552-53, 105 S.Ct. at 2226. In this case, the copyrighted computer program embedded in the U-30 chip descrambles satellite-transmitted programming for paying subscribers. The subject computer program secures plaintiffs-appellees’ product, audio-visual programming, for these subscribers, and it has copyright protection. Because the CMS computer program is copyrighted, a pirate chip copying this program and performing its function violates the copyright laws. Any decoding pirate chip is unlawful, not fair use. See also Harper & Row, 471 U.S. at 564, 105 S.Ct. at 2232 (“A use that so clearly infringes the copyright holder’s interests in confidentiality ... is difficult to characterize as ‘fair.’ ”); Duncan, 744 F.2d at 1497 (Even the societal importance of receipt of news did not save the copying and sale of a television station’s news reports as fair use.).

Regarding the third factor, the amount and substantiality of the portion of the copyrighted work used, the Supreme Court has directed a qualitative evaluation of the copying of the copyrighted work. Harper & Row, 471 U.S. at 564-65, 105 S.Ct. at 2233. That is, a small degree of taking is sufficient to transgress fair use if the copying is the essential part of the copyrighted work. See, e.g., Harper & Row, 471 U.S. at 539, 565-66, 105 S.Ct. at 2233 (13% of defendant’s article copied from plaintiff’s manuscript held sufficient for copyright infringement because it contained the heart of the book); Meeropol v. Nizer, 560 F.2d 1061, 1071 (2d Cir.1977) (although copyrighted letters were less than 1% of the infringing work, they were displayed prominently), cert. denied, 434 U.S. 1013, 98 S.Ct. 727, 54 L.Ed.2d 756 (1978); Roy Export Co. Establishment of Vaduz, Liechtenstein, Black, Inc. v. Columbia Broadcasting Sys., Inc., 503 F.Supp. 1137, 1145 (S.D.N.Y.1980) (fifty-five seconds taken from a one-hour and twenty-nine-minute film deemed qualitatively substantial for copyright infringement), aff'd, 672 F.2d 1095 (2d Cir.), cert. denied, 459 U.S. 826, 103 S.Ct. 60, 74 L.Ed.2d 63 (1982); see also Sheldon v. Metro-Goldwyn Pictures Corp., 81 F.2d 49, 56 (2d Cir.) (“[N]o plagiarist can excuse the wrong by showing how much of his work he did not pirate.”), cert. denied, 298 U.S. 669, 56 S.Ct. 835, 80 L.Ed. 1392 (1936). Furthermore, copying a substantial portion of the copyrighted work evidences the qualitative value of the copied work, both to the copyright owner and to the infringer “who seeks to profit from marketing someone else’s copyrighted expression.” Harper & Row, 471 U.S. at 565, 105 S.Ct. at 2233; see also Southern Bell, 756 F.2d at 810 (Substantial copying raises the issue of fair use.). The Dealer Demo chip, used and promoted by Kenny on Boresight, copies 86% of the CMS computer program within the U-30 chip. Because virtually all of the copyrighted work is used, evidenced by the essential or majority of the video picture being displayed, the fair-use defense is unavailing. See id.

The fourth factor, the effect on the potential market for or value of the copyrighted work, is considered by the Supreme Court as “undoubtedly the single most important element of fair use,” since a proper application of fair use does not impair materially the marketability of the copied work. Harper & Row, 471 U.S. at 566-67, 105 S.Ct. at 2233-34 (citing 1 Nimmer on Copyright § 1.10[D]). Under section 107, “potential market” means either an immediate or a delayed market, and includes harm to derivative works. Harper & Row, 471 U.S. at 568, 105 S.Ct. at 2234; Duncan, 744 F.2d at 1496. Plaintiffs-appellants’ business consists of selling programming to paying subscribers, and the subject, copyrighted CMS computer program secures their product for customers. Obviously, receipt of plaintiffs-appellees’ scrambled programming without payment injures their present and future customer markets, and denies them considerable revenue to which they are entitled for the services that they provide. See Harper & Row, 471 U.S. at 567, 105 S.Ct. at 2234.

Moreover, “every commercial use of copyrighted material is presumptively an unfair exploitation” of the copyright owner’s monopoly privilege. Sony, 464 U.S. at 451, 104 S.Ct. at 793; Duncan, 744 F.2d at 1496-97. On Boresight, Kenny openly touted the inroads that had been and could be made into the VideoCipher® II market as well as the profitability of pirate chips. The actual and future detrimental market effects coupled with the commercial-use presumption negates the fair-use defense. We, therefore, conclude that plaintiffs-ap-pellees’ unrefuted prima facie case of willful, direct copyright infringement merited summary judgment because none of the four statutory factors supported defendants-appellants’ affirmative defense of fair use.

b. Contributory Copyright Infringement

Contributory infringement necessarily must follow a finding of direct or primary infringement. 3 Nimmer on Copyright § 12.04[A] at 12-42 to -42.1. This court has stated the well-settled test for a contributory infringer as “ ‘one who, with knowledge of the infringing activity, induces, causes or materially contributes to the infringing conduct of another.’ ” Casella v. Morris, 820 F.2d 362, 365 (11th Cir.1987) (quoting Gershwin Publishing Corp. v. Columbia Artists Management, Inc., 443 F.2d 1159, 1162 (2d Cir.1971)); Columbia Pictures Indus., Inc. v. Redd Horne, Inc., 749 F.2d 154, 160 (3d Cir.1984); see also Sony, 464 U.S. at 437, 104 S.Ct. at 786 (The Supreme Court has defined a contributory infringer as one who “was in a position to control the use of copyrighted works by others and had authorized the use without permission from the copyright owner.”); 3 Nimmer on Copyright § 12.04 (generally discussing contributory infringement). Furthermore, this court explicated that “[t]he standard of knowledge is objective: ‘Know, or have reason to know.’ ” Ca- sella, 820 F.2d at 365 (quoting Gershwin, 443 F.2d at 1162). Contributory infringement will not be found if the product in question is capable of “substantial nonin-fringing uses,” the determinative issue in Sony, and clarified in that case as wide use “for legitimate, unobjectionable purposes.” Sony, 464 U.S. at 442, 104 S.Ct. at 789; see 3 Nimmer on Copyright § 12.04[A] at 12-42 to -45. In Sony, the Court was impressed by the district court’s finding that the petitioner, Sony Corporation, had not “influenced or encouraged” unlawful copies. Sony, 464 U.S. at 438, 104 S.Ct. at 787.

The facts in this case demonstrate that Kenny actually knew that the CMS computer program was copyrighted, and that he acted in direct defiance of this knowledge. Kenny encouraged the duplication of the CMS program of the U-30 chip by giving funds and equipment to Bepko and Ward in order to break the VideoCipher®II. In his descriptions of pirate chips on Boresight, he frequently warned that these chips were unlawful. Furthermore, Kenny recommended the purchase of pirate chips abroad in order to avoid American laws.

Even if he could prove that he did not know that the subject computer program was copyrighted, actual knowledge is not required. All that must be shown is that Kenny had reason to know. Casella, 820 F.2d at 365. At the Descrambling Summit, Cooper discussed the recent copyright infringement suit in Arizona, involving some of the plaintiffs-appellees in this case as well as a defendant from which Kenny had acquired a pirate chip. Additionally, an attorney there, as part of the instructive program, specifically addressed the inherent legal problems of pirate chips and advised that the use of pirate chips to break the VideoCipher® II would violate American copyright and communications laws. The Descrambling Summit was held outside the United States in order to avoid American laws, and attendees were informed that their distributed pirate chips could be mailed to them to evade the United States Customs Service.

There is ample, undisputed evidence in this case to show that defendants-appellants had actual or apparent knowledge that the CMS computer program located in the U-30 chip was copyrighted and that they were violating the copyright laws by promoting and selling pirate chips designed to break the VideoCipher®II. Furthermore, we find particularly reprehensible Kenny’s continuing to hawk pirate chips to his audiences not only after suit was filed in this case, but also following entry of the preliminary injunction. We are not persuaded by defendants-appellants’ arguments of noninfringing uses. While there may be other uses for some of the devices promoted by Kenny, we conclude that Kenny utilized and advertised these devices primarily as infringement aids and not for legitimate, noninfringing uses. An ostensible purpose of Boresight was to inform its audience of the latest developments in the pirate chip business and to instruct viewers in methods to compromise the VideoCi-pher®II by using pirate chips. Kenny even offered to install the socket in circuitry boards to facilitate the insertion of a pirate chip to replace the U-30 chip. Accordingly, we conclude that Kenny’s use of Boresight to promote various pirate chips as well as other infringing aids, and his participation in the Descrambling Summit constituted obtrusive contributory infringement, warranting granting summary judgment.

2. Communications Violations

The district court found defendants-appellants Kenny and Network liable for willful, for-profit violations of section 705 of the Federal Communications Act of 1934 (Communications Act), as amended, 47 U.S.C. section 605 (Supp. V 1987). Section 605(a) prohibits the unauthorized receipt, assistance in receiving, or further transmission of radio communications for benefit by a person (individual, partnership, association, joint-stock company, trust or corporation) or that of another unentitled individual or entity. 47 U.S.C. § 153(i) (1982); 47 U.S.C. § 605(a) (Supp. V 1987). “Radio communication,” as defined by section 3(b) of the Communications Act, has been interpreted to include television transmissions. 47 U.S.C. § 153(b) (1982); ON/TV of Chicago v. Julien, 763 F.2d 839, 842 (7th Cir.1985). The act of viewing subscription programming on a television set equipped with an unauthorized decoder has been held to be disclosure of the “ ‘existence, contents, substance, purport, effect, or meaning’ ” of the signal of the subscription television service to nonsubscribers. National Subscription Television v. S & H TV, 644 F.2d 820, 827 (9th Cir.1981) (quoting 47 U.S.C. § 605(a)). Under section 605(d)(4), the importation, manufacture, sale, or distribution of equipment intended to be used to assist in any intercepting and/or divulging activity proscribed by section 605(a) creates liability to the same penalties and remedies as-.the person or entity engaging in such prohibited activities.

The prohibitions of section 605, however, “shall not apply to the receiving, divulging, publishing, or utilizing the contents of any radio communication which is transmitted by any station for the use of the general public....” 47 U.S.C. § 605(a) (Supp. V 1987). Confronted with decoding or de-scrambling devices in the context of subscription television, other circuits have construed communication transmissions for the use of the general public to mean intended for, rather than available to, the general public in order to find unauthorized decoders violative of section 605. See, e.g., ON/TV, 763 F.2d at 842; Movie Sys., Inc. v. Heller, 710 F.2d 492, 494 (8th Cir.1983); National Subscription Television, 644 F.2d at 823-25; Chartwell Communications Group v. Westbrook, 637 F.2d 459, 465 (6th Cir.1980). We are persuaded by the rationale of the Seventh Circuit, affirming the grant of injunctive relief against the seller of decoder kits to unscramble plaintiffs subscription television signal:

ON/TV collects its revenues by renting decoders to its subscribers. Typically, viewers who purchase pirate decoders do so to evade paying the monthly rental fee to ON/TV. Thus, ON/TV loses a potential customer whenever a pirate decoder is sold. The sale of pirate decoders threatens the viability of the subscription television industry and there is no countervailing social or policy consideration that would justify these sales.

ON/TV, 763 F.2d at 844.

This circuit has addressed unauthorized viewing of certain satellite transmissions, including Showtime, by using an earth satellite dish owned in common by individual unit owners of a condominium association. Showtime/The Movie Channel, Inc. v. Covered Bridge Condominium Ass’n, Inc., 881 F.2d 983 (11th Cir.1989) (per curiam). This court held that section 605(a) “prohibits the unauthorized third party reception of satellite transmissions intended for fee-paying subscribers.” Id. at 988. Combining the statutory language, the interpretive reasoning of other circuits specifically addressing unauthorized decoding or descrambling devices for subscription television, and the decision by this court, we hold that section 605 readily applies to proscribe pirate chips and other unauthorized decoding devices, which enable third parties to receive television satellite transmissions intended for paying subscribers. National Subscription Television, 644 F.2d at 826; see also Chartwell Communications, 637 F.2d at 466 (“It is clear that by selling decoders or decoder schematics the appellees are assisting third parties in receiving communications to which they are not entitled.”).

Defendants-appellants have argued that sales of Dealer Demo chips and Bag-O-Parts kits do not violate section 605 because these devices descramble only the video portion of the satellite transmission and because the Dealer Demo chip overlays a portion of the video picture with a black box. These assertions, however, ignore the plain meaning of the statutory language, which defines “encrypt” as modifying aural, visual, or both transmissions to prevent unauthorized programming receipt. See National Subscription Television, 644 F.2d at 826-27. We conclude that defendants-appellants have not refuted their obvious violations of section 605.

Kenny’s words and demonstrations on Boresight encouraged and assisted third parties in their purchase and use of decoding devices to compromise the VideoCi-pher®II. Furthermore, he directly assisted Bepko and Ward with funds and equipment to aid them in the manufacture of pirate chips for the intended sale to and use by third parties. Kenny and those manufacturers of chips, whom he assisted, unquestionably profited from their activities. Kenny even bragged on Boresight that his charge for installing a socket in a circuitry board for easy removal of the U-30 chip was another way for him to make money. He also informed his audiences of the names and addresses of sources of pirate chips outside the United States. With such overwhelming, undisputed evidence, including Kenny’s words and actions, we conclude that the district court correctly granted summary judgment as to defendants-appellants’ willful and profitable communications violations of section 605. See Covered Bridge, 881 F.2d at 989.

3. The First Amendment Defense

From the outset of this litigation and their assertion of a First Amendment affirmative defense regarding both the copyright and communications violations, defendants-appellants have claimed that Kenny’s discussions on Boresight of the encryption technology, the existence and availability of pirate chips, and the Descrambling Summit amount to nothing more than informational reporting and editorial commentary, or protected speech. In their effort to support their defense of the public’s right to a free exchange of information and ideas, Kenny and Network have argued that their speech did not lose its protected character because some individuals may have listened to it, chosen to attend the summit, obtained pirate chips, and used them “to commit some illegal act.” Appellants’ Brief at 43. Furthermore, they assert that Kenny warned his audiences that the various decoding devices might be unlawful. Defendants-appellants protest that the final judgment and permanent injunction in this case constitute an unconstitutional application of statutory law to abridge their right to free speech.

With respect to copyright protection, “[t]he first amendment is not a license to trammel on legally recognized rights in intellectual property.” Dallas Cowboys, 600 F.2d at 1188. Since the Copyright Act is the congressional implementation of a constitutional directive to encourage inventors by protecting their exclusive rights in their discoveries, copyright interests also must be guarded under the Constitution, and injunctive relief is a common judicial response to infringement of a valid copyright. U.S. Const. art. I, § 8, cl. 8; Dallas Cowboys, 600 F.2d at 1187; see also Harper & Row, 471 U.S. at 555-60, 105 S.Ct. at 2228-30; Duncan, 744 F.2d at 1498-99 (discussing generally a refusal to revisit fair-use arguments under the guise of the First Amendment). In the context of communications law, a First Amendment right of access to transmitted signals argument has been rejected as to subscription television. California Satellite Sys. v. Seimon, 767 F.2d 1364, 1367-68 (9th Cir.1985). Upholding the injunctive relief, the court determined that the defendant enjoyed no right of access, when “the sole and exclusive use to which the defendant has put his equipment is the unlawful pirating of plaintiff's signal.” Id. at 1368. The court found that the district court’s injunction was targeted specifically at the infringing activity and, therefore, did not infringe on any First Amendment interests of the defendant. We also have determined that the permanent injunction entered in this case is limited in scope, including only defendants-appellants’ actions which violate section 605. See id.

Moreover, commercial speech, accorded lesser protection than other constitutionally guaranteed expression, may be banned if it relates to illegal activity. Central Hudson Gas & Electric Corp. v. Public Serv. Comm’n, 447 U.S. 557, 563-64, 100 S.Ct. 2343, 2350, 65 L.Ed.2d 341 (1980); Florida Businessmen for Free En ter. v. City of Hollywood, 673 F.2d 1213, 1217 (11th Cir.1982). Although defendants-appellants do not characterize their speech as commercial, we find that Kenny’s commentary, regarding various pirate chips and other decoding devices, appropriately comports with the Supreme Court’s description of commercial expression, which “not only serves the economic interest of the speaker, but also assists consumers and furthers the societal interest in the fullest possible dissemination of information.” Central Hudson, 447 U.S. at 561-62, 100 S.Ct. at 2349. The involvement of the First Amendment in commercial speech “is based on the informational function of advertising.” Central Hudson, 447 U.S. at 563, 100 S.Ct. at 2350. In this case, Kenny promoted descrambling devices for plaintiffs-appellees’ subscription programming, and assisted in the creation, advertisement and sale of pirated chips to compromise the copyrighted CMS program within the U-30 chip of the VideoCipher® II. “If that [commercial] activity is deemed ‘speech,’ then it is speech proposing an illegal transaction, which a government may regulate or ban entirely.” Village of Hoffman Estates v. Flipside, Hoffman Estates, Inc., 455 U.S. 489, 496, 102 S.Ct. 1186, 1192, 71 L.Ed.2d 362 (1982); see also Pittsburgh Press Co. v. Pittsburgh Comm’n on Human Relations, 413 U.S. 376, 389, 93 S.Ct. 2553, 2561, 37 L.Ed.2d 669 (1973) (“Any First Amendment interest which might be served by advertising an ordinary commercial proposal and which might arguably outweigh the governmental interest supporting the regulation is altogether absent when the commercial activity itself is illegal and the restriction on advertising is incidental to a valid limitation on economic activity.”).

Because we have concluded that Kenny’s commercial speech through Network not only violated the copyright and communications laws, but also encouraged third parties to do so, we hold that defendants-appellants have no protection under the First Amendment for their unlawful expression. Kenny’s weak warnings of illegality are meaningless in his overall sales pitch, especially when he was aware that pirate chips and decoding devices were unlawful and advised his audience on methods to evade American laws, such as purchase abroad. Since the First Amendment provides no defense to Kenny and Network, our conclusion that summary judgment was proper as to their violation of the copyright and communications laws stands.

B. The Award of Statutory Damages Without Trial

The district court’s final judgment and decree of permanent injunction awarded plaintiffs statutory damages of $20,-000.00 against defendants Kenny, Network and Cooper based on their willful, direct and contributory copyright infringements and for-profit violations of the communications laws. The district court also awarded plaintiffs additional statutory damages against Kenny and Network for their separate willful, for-profit communications violations. As a procedural matter, the plaintiff copyright owner must have registered the copyright prior to the infringement in order to obtain statutory damages. 17 U.S.C. § 412 (1982); Evans Newton Inc. v. Chicago Sys. Software, 793 F.2d 889, 897 (7th Cir.), cert. denied, 479 U.S. 949, 107 S.Ct. 434, 93 L.Ed.2d 383 (1986).

Both the copyright and communications statutes allow the aggrieved party to elect either actual or statutory damages. 17 U.S.C. § 504(b), (c) (1982); 47 U.S.C. § 605(d)(3)(C)(i) (Supp. V 1987). Under each statute at the time of this action, the statutory damages to be awarded per copyright infringement or communications violation are not less than $250.00 or more than $10,000.00, “as the court considers just.” 17 U.S.C. § 504(c)(1); 47 U.S.C. § 605(d)(3)(C)(i)(II). In this case, plaintiffs elected statutory damages, which they may choose whether or not adequate evidence exists as to the actual damages incurred by plaintiffs or the profits gained by defendants. Harris v. Emus Records Corp., 734 F.2d 1329, 1335 (9th Cir.1984); 3 Nimmer on Copyright § 14.04[A]. Generally, statutory damages are awarded when no actual damages are proven, or actual damages and profits are difficult or impossible to calculate. F.W. Woolworth Co. v. Con temporary Arts, Inc., 344 U.S. 228, 231-33, 73 S.Ct. 222, 224-25, 97 L.Ed.2d 276 (1952); Warner Bros. Inc. v. Dae Rim Trading, Inc., 877 F.2d 1120, 1126 (2d Cir.1989). Plaintiffs-appellees have represented that profits could not be calculated because of defendants-appellants’ failure to produce the necessary documentation.

The Copyright Act provides that “where the copyright owner sustains the burden of proving, and the court finds, that infringement was committed willfully, the court in its discretion may increase the award of statutory damages to a sum of not more than $50,000.00” for each infringement. 17 U.S.C. § 504(c)(2); Fitzgerald Publishing Co. v. Baylor Publishing Co., 807 F.2d 1110, 1116-17 (2d Cir.1986). “Willfully,” in the context of section 504(c)(2), means that the defendant “knows his actions constitute an infringement; the actions need not have been malicious.” Broadcast Music, Inc. v. Xanthas, Inc., 855 F.2d 233, 236 (5th Cir.1988); RCA/Ariola Int’l, Inc. v. Thomas & Grayston Co., 845 F.2d 773, 779 (8th Cir.1988); 3 Nimmer on Copyright § 14.04[B][3]; see also Fitzgerald Publishing Co., 807 F.2d at 1117 (“The statute does not distinguish between those who maliciously infringe another’s copyright or those who simply act knowing that they are infringing upon the copyright.”). Furthermore, when the infringement is willful, “deterrence of future violations is a legitimate consideration” because “ ‘defendants must not be able to sneer in the face of copyright owners and copyright laws.’ ” International Korwin Corp. v. Kowalczyk, 855 F.2d 375, 383 (7th Cir.1988) (quoting and affirming International Korwin Corp. v. Kowalczyk, 665 F.Supp. 652, 659 (N.D.Ill.1987)); see F.W. Woolworth Co., 344 U.S. at 233, 73 S.Ct. at 225. In this case, we have no doubt that Kenny knew that M/A-COM’s CMS program within the U-30 chip was copyrighted and that he not only assisted in the production of pirate chips by giving funds and equipment to Bepko and Ward, but also that he openly publicized and encouraged the purchase of these pirate chips as well as others on Boresight in blatant defiance of the copyright laws. Given the alleged educational function of Boresight and Kenny’s touted knowledge of the satellite programming industry, any assertions that he did not know that the CMS program of the U-30 chip was copyrighted are not credible.

Under the Communications Act, in a case where the court finds “that the violation was committed willfully and for purposes of direct or indirect commercial advantage or private financial gain, the court in its discretion may increase the award of damages, whether actual or statutory, by an amount of not more than $50,-000.00.” 47 U.S.C. § 605(d)(3)(C)(ii). The Supreme Court’s definition of “willful” in the context of a civil statute as conduct showing “ ‘disregard for the governing statute and an indifference to its requirements’ ” has been utilized for communications violations under section 605. ON/TV, 763 F.2d at 844 (quoting Trans World Airlines, Inc. v. Thurston, 469 U.S. 111, 127, 105 S.Ct. 613, 625, 83 L.Ed.2d 523 (1985)). Commercial advantage or private financial gain is not pertinent to finding a violation of section 605(a), but is material in determining an enhanced civil damage award. 47 U.S.C. § 605(d)(3)(C)(ii).

Kenny’s flagrant violations of section 605 show his disregard for the statutory requirements with which he was familiar given his knowledge of the satellite programming industry and the information that he disseminated over Boresight. He has conceded that his sole source of income during 1986 was proceeds from his Bag-O-Parts business, and that he profited more than $17,000.00 from sales of Bag-O-Parts and various chips advertised on Boresight. Kenny also has admitted that he was paid $14,500.00 to videotape the instructive sessions at the Descrambling Summit. The anticipated receipt of additional revenues from videotape sales provided Kenny and Network a significant financial incentive for promoting the Descrambling Summit on Boresight in order to assure its success. Furthermore, Kenny openly referred to his monetary interests in publicizing on Bore-sight his various devices and services, such as removing the U-30 chip from a customer's circuitry board and installing a socket to facilitate the insertion of pirate chips. We have no difficulty in determining that defendants-appellants’ section 605 violations were willfully committed for direct and indirect financial gain not only because of Kenny’s boastful statements to this effect on Boresight, but also because of the actual profits obtained from these violations.

“[T]he employment of the statutory yardstick, within set limits, is committed solely to the court which hears the case, and this fact takes the matter out of the ordinary rule with respect to abuse of discretion.” Douglas v. Cunningham, 294 U.S. 207, 210, 55 S.Ct. 365, 366, 79 L.Ed. 862 (1935); see also Xanthas, 855 F.2d at 237 (“The statute by its terms places no further limits on the district court’s discretion.”); Harris, 734 F.2d at 1335 (“The court has wide discretion in determining the amount of statutory damages to be awarded, constrained only by the specified maxima and minima.” (citing L.A. Westermann Co. v. Dispatch Printing Co., 249 U.S. 100, 39 S.Ct. 194, 63 L.Ed. 499 (1919))). In awarding statutory damages, the court “may take into account the attitude and conduct of the parties.” Warner Bros., 877 F.2d at 1126; see also F.W. Woolworth Co., 344 U.S. at 233, 73 S.Ct. at 225 (“The statutory rule ... is designed to discourage wrongful conduct_ Even for uninjurious and unprofitable invasions of copyright the court may, if it deems it just, impose a liability within statutory limits to sanction and vindicate the statutory policy.”); Fitzgerald Publishing Co., 807 F.2d at 1117 (“[T]he potential for discouraging the defendant is factored into the determination of the award.”). In its broad discretion for determining statutory damages, the district court should consider both the willfulness of the defendant’s conduct and the deterrent value of the sanction imposed. In this ease, we are mindful not only of Kenny’s open promotion on Boresight of the purchase of pirate chips and other devices to compromise the VideoCipher®II, but also of his continued advertisements following entry of the preliminary injunction. Cf. Transgo, Inc. v. Ajac Transmission Parts Corp., 768 F.2d 1001, 1022-23 (9th Cir.1985) (The court held an infringer in civil contempt for violating an injunction for using a trademark name and imposed investigation costs.), cert. denied, 474 U.S. 1059, 106 S.Ct. 802, 88 L.Ed.2d 778 (1986).

The district court did not describe how it arrived at the statutory damages that it awarded by clarifying the number of copyright infringements and communications violations which occurred and the value within the statutory limits assigned to each infringement or violation, as some courts meticulously have done. See, e.g., Xanthas, 855 F.2d at 236, 240. While an explanation would have been helpful, we cannot say that the joint and several award of $20,000.00 against Kenny, Network and Cooper for willful, direct and contributory copyright infringements and for-profit communications violations as well as the $110,-000.00 award against Kenny and Network for separate willful, for-profit communications violations are outside the statutory limitations under various combinations of the number of infringements and communications violations multiplied by the court’s assigned values under the respective statutes. We cannot justify remand and the expenditure of judicial effort in order to delineate numbers and values for infringements and communications violations when the resulting statutory award likely would remain the same. Given the wide latitude accorded the district court in awarding statutory damages, bounded only by the statutory limits, and especially with defendants-appellants’ conduct warranting enhancement under both statutes, we hold that the statutory awards by the district court are not an abuse of discretion. Harris, 734 F.2d at 1335.

Defendants-appellants complain on appeal that they were entitled to a bench or jury trial on the issue of statutory damages. We quickly dispense with this contention. The former Fifth Circuit has held that, in an equitable copyright infringement action seeking only minimum statutory damages and injunctive relief, there is “no constitutional or statutory right to a jury trial.” Twentieth Century Music Corp. v. Frith, 645 F.2d 6, 7 (5th Cir. Unit B May 1981) (per curiam). Accordingly, we now hold that the latitude granted the district court’s great discretion in awarding statutory damages does not entitle defendants to a jury or bench trial as to an award of damages within the statutory limits of both the Copyright Act and the Communications Act, provided that the parties may submit all of their supporting evidence to the district court.

C. The Award of Attorneys’ Fees

The district court awarded $451,789.06 in attorneys’ fees and costs, after reviewing and adopting the magistrate’s report and recommendation. The magistrate independently reviewed the entire record and conducted an evidentiary hearing, including expert testimony, in making his determination. He was impressed by the deletions that plaintiffs made in their attorneys’ fee request, such as investigation of original claims subsequently abandoned and settlement negotiations with other defendants. He also was influenced by the value to M/A-COM and Cable/Home of the copyrighted CMS program, evidenced by revenue generated from sales of the VideoCi-pher®II, and their desire to protect against infringement. The magistrate considered the precedential Johnson factors in deciding upon the award. Johnson v. Georgia Highway Express, Inc., 488 F.2d 714, 717-19 (5th Cir.1974).

With the prerequisite of a registered copyright before infringement, the Copyright Act explicitly provides that “the court in its discretion may allow the recovery of full costs by or against any party ... [and] may also award a reasonable attorney’s fee to the prevailing party as part of the costs.” 17 U.S.C. §§ 412, 505; Sony, 464 U.S. at 434, 104 S.Ct. at 784. An attorneys’ fee award is “generally discretionary, seldom mandatory.” Casella, 820 F.2d at 366. In this circuit, a showing of bad faith or frivolity is not a precondition to awarding attorneys’ fees. Id.; Original Appalachian Artworks, Inc. v. Toy Loft, Inc., 684 F.2d 821, 832 (11th Cir.1982). We have adhered to the only two statutory requirements: the fee award should be granted to the prevailing party and the amount should be reasonable. Casella, 820 F.2d at 366; Original Appalachian Artworks, 684 F.2d at 832.

Generally, the prevailing party under the attorneys’ fee authorization of section 505 of the Copyright Act is identified as the party succeeding on a significant litigated issue that achieves some of the benefits sought by that party in initiating the suit. Warner Bros., 877 F.2d at 1126; see Hensley v. Eckerhart, 461 U.S. 424, 429, 433, 103 S.Ct. 1933, 1937, 1939, 76 L.Ed.2d 40 (1983); Hartman v. Hallmark Cards, Inc., 833 F.2d 117, 122 (8th Cir.1987). “A party's success on a claim that is ‘purely technical or de minimis’ does not qualify him as a ‘prevailing party.’ ” Warner Bros., 877 F.2d at 1126 (quoting Texas State Teachers Ass’n v. Garland Indep. School Dist., — U.S. -, 109 S.Ct. 1486, 1492, 103 L.Ed.2d 866 (1989)). Given plaintiffs-appellees’ success in protecting the subject copyrights and their programming, the principal objectives of this lawsuit, we have no difficulty in concluding that they are the prevailing parties in this action.

In this circuit, the reasonableness of the attorneys’ fee award is controlled by consideration of the Johnson factors. Southern Bell, 756 F.2d at 813; see United Feature Syndicate, Inc. v. Sunrise Mold Co., 569 F.Supp. 1475, 1481 (S.D.Fla.1983). Furthermore, while willfulness does not compel a fee award, it is an “important factor” in the district court’s “discretionary decisionmaking.” Casella, 820 F.2d at 366; see also Roulo v. Russ Berrie & Co., 886 F.2d 931, 942 (7th Cir.1989), cert. denied, — U.S. -, 110 S.Ct. 1124, 107 L.Ed.2d 1030 (1990); International Korwin, 855 F.2d at 384 (The Seventh Circuit has determined that a finding of willfulness will support an attorneys’ fee award.). The magistrate, to whom the district judge referred this case for the specific purpose of recommending an attorneys’ fee award, not only reviewed the entire record, but also conducted an evidentiary hearing on this issue. His report and recommendation explained that he weighed the Johnson factors in determining the attorneys’ fee award and that he was concerned with defendants’ flagrantly willful conduct. See Casella, 820 F.2d at 366-67; Southern Bell, 756 F.2d at 813. This recommendation was reviewed and adopted by the district court. Thus, we are presented with a detailed explanation and basis for the award, which is supported fully by the record. The ruling completely complies with the discretion accorded under section 505. Southern Bell, 756 F.2d at 813; Frith, 645 F.2d at 7; see also Casella, 820 F.2d at 367 (This court remanded the case to the district court to reconsider the attorneys’ fee issue and to “articulate its rationale for granting or denying attorney’s fees.”).

Furthermore, we are concerned, as were the reviewing magistrate and district court, with defendants-appellants’ outrageously willful conduct in assisting in the development of pirate chips, advertising these pirate chips and other devices, participating at the Descrambling Summit for the purpose of compromising the VideoCipher®II, and instructing Boresight audiences on ways to break the VideoCipher@II, in blatant disregard of the copyright laws. We view defendants-appellants’ willfulness as an important factor in the district court’s attorneys’ fee award. See Casella, 820 F.2d at 366; Lieb v. Topstone Indus., Inc., 788 F.2d 151, 156 (3d Cir.1986). As we have stressed, “ ‘the court’s choice of discretionary ruling should be in furtherance of the policies of the law that are being enforced, as informed by the court’s familiarity with the matter in litigation and the interest of justice.’ ” Casella, 820 F.2d at 367 (quoting S.C. Johnson & Son, Inc. v. Carter-Wallace, Inc., 781 F.2d 198, 201 (Fed.Cir.1986)).

D. Denial of the Motion to Dismiss for Lack of Personal Jurisdiction

Defendants-appellants Kenny and Network have claimed that the district court erred in denying their motion to dismiss on the basis of personal jurisdiction. They have argued that neither is a citizen of Florida and that they do not engage in business, or have offices, agents or employees in Florida. Additionally, defendants-appellants assert that the transmission of their programming into the state does not constitute the conduct of substantial activities within the state. The district court denied defendants-appellants’ motion to dismiss, based on lack of personal jurisdiction as well as other grounds, in an omnibus order without explanation.

Our review of the denial of a motion to dismiss founded on lack of personal jurisdiction is de novo. See Alexander Proudfoot Co. World Headquarters L.P. v. Thayer, 877 F.2d 912, 916 (11th Cir.1989). When the district court does not conduct a discretionary evidentiary hearing on a motion to dismiss for lack of personal jurisdiction, the plaintiff must establish a prima facie case of personal jurisdiction over the nonresident defendant. Morris v. SSE, Inc., 843 F.2d 489, 492 (11th Cir.1988); Delong Equip. Co. v. Washington Mills Abrasive Co., 840 F.2d 843, 845 (11th Cir.1988). “A prima facie case is established if the plaintiff presents sufficient evidence to defeat a motion for directed verdict.” Morris, 843 F.2d at 492. The district court must accept the facts alleged in the complaint as true, to the extent that they are uncontroverted by the defendant’s affidavits. Id.; Delong Equip. Co., 840 F.2d at 845. Where the parties’ affidavit and deposition evidence conflict, the district court must construe all reasonable inferences in favor of the plaintiff. Morris, 843 F.2d at 492; Delong Equip. Co., 840 F.2d at 845.

The determination of personal jurisdiction over a nonresident defendant requires a two-part analysis by the federal courts. Alexander Proudfoot Co., 877 F.2d at 919; see Omni Capital Int’l, Ltd. v. Rudolf Wolff & Co., 484 U.S. 97, 104-05, 108 S.Ct. 404, 409-10, 98 L.Ed.2d 415 (1987); Williams Electric Co. v. Honeywell, Inc., 854 F.2d 389, 391 (11th Cir.1988) (per curiam); Delong Equip. Co., 840 F.2d at 847. First, we must examine the jurisdictional issue under the state long-arm statute. Alexander Proudfoot Co., 877 F.2d at 919; Delong Equip. Co., 840 F.2d at 847; see Omni Capital Int’l, 484 U.S. at 104-05, 108 S.Ct. at 409-10; Williams Electric Co., 854 F.2d at 391. Second, we must ascertain whether or not sufficient “minimum contacts” exist to satisfy the Due Process Clause of the Fourteenth Amendment so that “maintenance of the suit does not offend ‘traditional notions of fair play and substantial justice.’ ” International Shoe Co. v. Washington, 326 U.S. 310, 316, 66 S.Ct. 154, 158, 90 L.Ed. 95 (1945) (quoting Milliken v. Meyer, 311 U.S. 457, 463, 61 S.Ct. 339, 342, 85 L.Ed. 278 (1940)); Alexander Proudfoot Co., 877 F.2d at 919; see Omni Capital Int’l, 484 U.S. at 104, 108 S.Ct. at 409; Williams Electric Co., 854 F.2d at 391; Delong Equip. Co., 840 F.2d at 847.

When jurisdiction is based on a federal question arising under a statute that is silent regarding service of process, Rule 4(e) of the Federal Rules of Civil Procedure requires that both assertion of jurisdiction and service of process be determined by state amenability standards, or the state long-arm statute. Max Daetwyler Corp. v. R. Meyer, 762 F.2d 290, 295 (3d Cir.), cert. denied, 474 U.S. 980, 106 S.Ct. 383, 88 L.Ed.2d 336 (1985); DeMelo v. Toche Marine, Inc., 711 F.2d 1260, 1265-66 (5th Cir.1983); see Omni Capital Int’l, 484 U.S. at 105, 108 S.Ct. at 410; Delong Equip. Co., 840 F.2d at 847. While jurisdiction exists in the district court for copyright and communications statutory violations, there is no service of process provision for either statute. See 28 U.S.C. §§ 1331, 1338 (1982). Accordingly, Rule 4(e) directs us to the Florida long-arm statute in order to determine the amenability of nonresident defendants-appellants to jurisdiction in Florida. Fla.Stat. § 48.193 (1987); see Bangor Punta Operations, Inc. v. Universal Marine Co., 543 F.2d 1107, 1108 (5th Cir.1976); see also Rebozo v. Washington Post Co., 515 F.2d 1208, 1212 (5th Cir.1975) (The intent of the Florida long-arm statute has been interpreted to “further facilitate the state’s power to act extraterritorially.”).

Since the extent of the long-arm statute is governed by Florida law, “federal courts are required to construe it as would the Florida Supreme Court.” Oriental Imports & Exports, Inc. v. Maduro & Curiel’s Bank, N.V., 701 F.2d 889, 890-91 (11th Cir.1983). The Florida Supreme Court has explicated section 48.193, explaining that complying with the long-arm statute and determining federal constitutional minimum contacts are discrete analy-ses:

By enacting section 48.193, the legislature has determined the requisite basis for obtaining jurisdiction over nonresident defendants as far as Florida is concerned. It has not specifically addressed whether the federal constitutional requirement of minimum contacts has been met. As a practical matter, it could not do so because each case will depend upon the facts.

Venetian Salami Co. v. Parthenais, 554 So.2d 499, 500 (Fla.1989). Without addressing the potential appropriateness of other provisions of the Florida long-arm statute to nonresidents Kenny and Network, we limit our analysis to the tortious act provision because it is applicable and sufficient. Fla.Stat. § 48.193(l)(b).

Nonresident defendants have been found liable under the tortious act provision when the precise location of the alleged tort within the state has been difficult to identify. See Oriental Imports & Exports, 701 F.2d at 894. In Rebozo and Bangor Punta, the respective torts of alleged libel in an out-of-state newspaper circulated in Florida and violation of property rights in building trawlers advertised and sold by a foreign corporate defendant in Florida constituted tortious acts under the long-arm statute. The former Fifth Circuit stressed that “the breach of a common law copyright subjects the wrongdoer to liability in tort” within the reach of the Florida long-arm statute. Bangor Punta, 543 F.2d at 1109. Additionally, the long-arm statute is not limited to an act in Florida causing injury in Florida, but includes “the situation in which a foreign tortious act causes injury within the forum.” Rebozo, 515 F.2d at 1212; Bangor Punta, 543 F.2d at 1109; see also Edy Clover Prods., Inc. v. National Broadcasting Co., 572 F.2d 119 (3d Cir.1978) (On an interlocutory appeal from a denial of a motion to dismiss based on lack of personal jurisdiction, the court found no unfairness in requiring a television producer to answer a copyright infringement charge in a remote forum receiving the broadcast.); German Educ. Television Network, Ltd. v. Oregon Pub. Broadcasting Co., 569 F.Supp. 1529, 1532 (S.D.N.Y.1983) (Satellite transmissions, intended for all public broadcasting stations and beamed into New York, were “the Star Wars equivalent of the United States Postal Service” and subjected marketers of infringing programming proposals to personal jurisdiction under New York’s tortious act provision, despite no evidence of the marketers’ presence in New York.). “The crucial matter is whether the individual defendant can be held personally liable for acts committed in the forum, not whether his contacts with the forum arose in his personal capacity.” Delong Equip. Co., 840 F.2d at 852.

In this case, we have found violations of both the copyright and communications laws. This court has recognized that “[f]or personal jurisdiction to attach under the ‘tortious activity’ provision of the Florida long-arm statute, the plaintiff must demonstrate that the non-resident defendant ‘committed a substantial aspect of the alleged tort in Florida’ by establishing that the activities in Florida ‘w[ere] essential to the success of the tort.’ ” Williams Electric Co., 854 F.2d at 394 (quoting Watts v. Haun, 393 So.2d 54, 56 (Fla.Dist.Ct.App.1981)). The cumulative receipt of Bore-sight programming, which caused the purchase of pirate chips and other devices to compromise the VideoCipher®II for the profit of defendants-appellants, made the sales in individual states essential. We, therefore, find that the Boresight broadcasts, which stimulated Florida purchases in violation of the copyright and communications laws, were substantial. Furthermore, connections through a Florida travel agent were essential for attending the Descrambling Summit, which Kenny promoted through Boresight and from which he derived profits. Given these tortious acts committed by defendants-appellants in Florida, we conclude that section 48.-193(l)(b) is applicable to them.

Having found the tortious act provision of the Florida long-arm statute applicable to defendants-appellants, we must analyze this long-arm jurisdiction under the due process requirements of the federal constitution. The Florida Supreme Court has acknowledged that “[t]he mere proof of any one of the several circumstances enumerated in section 48.193 as the basis for obtaining jurisdiction of nonresidents does not automatically satisfy the due process requirement of minimum contacts,” although implicit within some of the provisions are sufficient facts, which, if proved, would suffice. Venetian Salami Co., 554 So.2d at 502. This court has recognized that the instruction of International Shoe Co. and its progeny is that the determination of whether or not the assumption of personal jurisdiction over a nonresident defendant conforms with due process requires a dual analysis: first, we must ascertain if defendants-appellants have established “ ‘minimum contacts’ ” with Florida, the forum state; second, we must decide if the exercise of personal jurisdiction over nonresident defendants-appellants in Florida would offend “ ‘traditional notions of fair play and substantial justice.’ ” Williams Electric Co., 854 F.2d at 392 (quoting International Shoe Co., 326 U.S. at 316, 66 S.Ct. at 158); Morris, 843 F.2d at 492; Delong Equip. Co., 840 F.2d at 853.

The nonresident defendant’s establishing “minimum contacts” in the forum state remains the “constitutional touchstone.” Burger King Corp. v. Rudzewicz, 471 U.S. 462, 474, 105 S.Ct. 2174, 2183, 85 L.Ed.2d 528 (1985); International Shoe Co., 326 U.S. at 316, 66 S.Ct. at 158. A forum may exercise specific jurisdiction over a nonresident defendant if the defendant has “ ‘purposefully directed’ ” his activities to forum residents and the resulting litigation derives from alleged injuries that “ ‘arise out of or relate to’ ” those activities. Burger King Corp., 471 U.S. at 472, 105 S.Ct. at 2182 (quoting Helicopteros Nacionales de Colombia, S.A. v. Hall, 466 U.S. 408, 414, 104 S.Ct. 1868, 1872, 80 L.Ed.2d 404 (1984) and Keeton v. Hustler Magazine, Inc., 465 U.S. 770, 774, 104 S.Ct. 1473, 1478, 79 L.Ed.2d 790 (1984)); Williams Electric Co., 854 F.2d at 392; Delong Equip. Co., 840 F.2d at 853. To comport with due process foreseeability, the nonresident’s “conduct and connection with the forum State are such that he should reasonably anticipate being haled into court there.” World-Wide Volkswagen Corp. v. Woodson, 444 U.S. 286, 297, 100 S.Ct. 559, 567, 62 L.Ed.2d 490 (1980); Burger King Corp., 471 U.S. at 474, 105 S.Ct. at 2183; Williams Electric Co., 854 F.2d at 392.

Determining minimum contacts requires examining the “quality and nature” of the nonresident defendant’s activity, with the essential finding that the defendant has “purposefully avail[ed] itself of the privilege of conducting activities within the forum State, thus invoking the benefits and protections of its laws.” Hanson v. Denckla, 357 U.S. 235, 253, 78 S.Ct. 1228, 1240, 2 L.Ed.2d 1283 (1958); see Burger King Corp., 471 U.S. at 474-75, 105 S.Ct. at 2183; Pesaplastic, C.A. v. Cincinnati Milacron Co., 750 F.2d 1516, 1522 (11th Cir.1985); Rubaii v. Lakewood Pipe of Texas, Inc., 695 F.2d 541, 544 (11th Cir.1983); Rebozo, 515 F.2d at 1214. A significant single act or meeting in the forum state has been held sufficient for personal jurisdiction there. Burger King Corp., 471 U.S. at 475, 105 S.Ct. at 2183; Helicopteros Nacionales, 466 U.S. at 417, 104 S.Ct. at 1873; Williams Electric Co., 854 F.2d at 392-93; Sea Lift, Inc. v. Refinadora Costarricense de Petroleo, S.A., 792 F.2d 989, 993 (11th Cir.1986). In our technologically sophisticated world permitting interstate business transactions by mail, wire and satellite signals, physical presence by the nonresident defendant is not necessary for personal jurisdiction in the forum state. See Burger King Corp., 471 U.S. at 476, 105 S.Ct. at 2184; Morris, 843 F.2d at 495.

Guided by these constitutional principles, we examine defendants-appellants’ activities in Florida. Weekly, Bore-sight programming was directed purposefully to Florida as well as to the rest of the broadcast area. Because arrangements for and transportation to and from the De-scrambling Summit, in which defendants-appellants participated, were through a Florida travel agent, the benefits and protections of that state were utilized. Therefore, Florida has a reasonable interest in this litigation. We find that the quality and nature of defendants-appellants’ activities in Florida included instruction on methods for compromising the VideoCipher®II, advertisement and sale of pirate chips, other devices and services for that purpose, culminating in the Descrambling Summit. All of these activities, violating the copyright and communications laws, are determinative of the amenability of defendants-appellants to personal jurisdiction in Florida. We are convinced that defendants-appellants had constitutional minimum contacts with Florida for personal jurisdiction there.

Having determined that defendants-appellants have sufficient minimum contacts with Florida, we must complete our analysis by ascertaining whether or not the exercise of personal jurisdiction over defendants-appellants would transgress traditional notions of fair play and substantial justice. “When minimum contacts have been established, often the interests of the plaintiff and the forum in the exercise of jurisdiction will justify even the serious burdens placed on the alien defendant.” Asahi Metal Indus. Co. v. Superior Court, 480 U.S. 102, 114, 107 S.Ct. 1026, 1034, 94 L.Ed.2d 92 (1987); Williams Electric Co., 854 F.2d at 393; see also Burger King Corp., 471 U.S. at 477, 105 S.Ct. at 2184-85 (“[Wjhere a defendant who purposefully has directed his activities at forum residents seeks to defeat jurisdiction, he must present a compelling case that the presence of some other considerations would render jurisdiction unreasonable.”). Furthermore, “modern transportation and communication have made it much less burdensome for a party sued to defend himself in a State where he engages in economic activity.” McGee v. International Life Ins. Co., 355 U.S. 220, 223, 78 S.Ct. 199, 201, 2 L.Ed.2d 223 (1957); Burger King Corp., 471 U.S. at 474, 105 S.Ct. at 2183; Williams Electric Co., 854 F.2d at 393. Significantly, a purposeful journey to Florida for a reason related to the litigation has been considered a deliberate choice placing defendants on notice that they were subject to suit in Florida. Williams Electric Co., 854 F.2d at 393.

Defendants-appellants have not presented compelling reasons for finding that personal jurisdiction in Florida would be unreasonable. They purposefully have directed unlawful activity in violation of the copyright and communications laws to Florida. Moreover, Kenny traveled to Florida in order to participate in the Descrambling Summit, the purpose of which was to instruct in further deliberate violations of the copyright and communications laws and from which defendants-appellants profited.

We find applicable the reasoning of the former Fifth Circuit in an analogous case, where the out-of-state defendant sought to escape liability on the basis of lack of personal jurisdiction:

The legal principle urged upon us by appellants would allow a publisher, fully aware of the strong possibility of resulting legal action, to print libelous matters directed at persons in distant localities, yet remain free from suit in such localities in spite of the pecuniary benefits gained in that very jurisdiction where it asserts it cannot be held legally accountable.

Rebozo, 515 F.2d at 1215 (quoting Curtis Publishing Co. v. Golino, 383 F.2d 586, 591 (5th Cir.1967)). Holding defendants-appellants amenable to personal jurisdiction in Florida does not contravene basic notions of fair play and substantial justice. Furthermore, we conclude that plaintiffs-appellees have established a personal jurisdiction prima facie case, which defendants-appellants have not rebutted convincingly. Our review of the record does not leave us with the “ ‘definite and firm conviction that a mistake has been committed’ ” by the district court in denying the motion by Kenny and Network to dismiss for lack of persona] jurisdiction; we agree that the district court did have personal jurisdiction over them. Williams Electric Co., 854 F.2d at 393 (quoting Anderson v. City of Bessemer City, 470 U.S. 564, 573, 105 S.Ct. 1504, 1511, 84 L.Ed.2d 518 (1985)).

E. Denial of the Motion for Additional Time to Respond to Plaintiffs’ Motion for Summary Judgment

Defendants-appellants complain that they were “severely prejudiced” by the district court’s “forc[ing]” them to respond to plaintiffs’ summary judgment motion within ten days, shortly after their recent acquisition of new counsel. Appellants’ Reply Brief at 25. We note that the subject motion was defendants’ second request for enhanced time to respond to plaintiffs’ summary judgment motion. Their first motion for an extension of time was denied because of their repeated failure to comply with court orders and local rules. Although the district court granted plaintiffs’ unopposed motion for summary judgment, it allowed their new counsel ten days to file an opposition. We are aware that defendants’ Rule 59(e) motion, based upon their failure to respond timely because of the acquisition of new counsel, also was dilatory. Despite the district court’s admonition that no additional response time would be allowed, defendants’ new counsel moved for an additional ten days to respond to plaintiffs’ summary judgment motion. This request was denied by the district court. Interestingly, defendants’ counsel filed their opposition to plaintiffs’ summary judgment motion within the first extension of time granted by the district court.

We find that the district court was abundantly generous with the time that it granted defendants to file a response to plaintiffs’ summary judgment motion in the face of obstructionist and delinquent conduct by defendants. This appellate issue by defendants-appellants is completely without merit. We conclude that the district court’s denial of a second request for extension of time to respond to plaintiffs’ summary judgment motion, after it had advised that it would not do so when granting an extension pursuant to defendants’ Rule 59(e) motion, was not an abuse of discretion because it was not arbitrary or unreasonable. See Hashwani v. Barbar, 822 F.2d 1038, 1040 (11th Cir.1987) (per curiam) (affirming denial of the continuance of a summary judgment hearing as being within the broad discretion of the district court); see also Instituto Nacional de Comercializacion Agricola v. Continental Illinois Nat’l Bank & Trust Co., 858 F.2d 1264, 1271-72 (7th Cir.1988); United States v. Kasuboski, 834 F.2d 1345, 1351-52 (7th Cir.1987) (finding no abuse of discretion by the district court in not allowing an extension of time to oppose a summary judgment motion).

In summary, the district court’s orders granting summary judgment to plaintiffs-appellees, awarding them damages without trial, awarding them requested attorneys’ fees, denying defendants-appellants’ motion to dismiss for lack of personal jurisdiction, and denying their motion for a second extension of time to respond to plaintiffs’ summary judgment motion are AFFIRMED. 
      
      . The Three Musketeers chip was described on Boresight as a method whereby you pay for one service and obtain all services, or a "one-for-all and all-for-one device.” Boresight News Transcript at 3 (Dec. 4, 1986). R3-80-Ex.D-3. In contrast, Kenny described the clone method as being where one VideoCipher®II is used to subscribe to all services "and that ID number that subscribes to everything, is then put into as many as a million other VC-IIs [VideoCi-pher®II]. The other million don't pay, just that one pays." Id. at 10.
     
      
      . Deposition of Shaun Kenny at 108. Ex.B-108.
     
      
      . Deposition of Shaun Kenny at 148. Ex.B-148.
     
      
      . Boresight News Transcript at 15, 16 (Dec. 4, 1986). R3-80-Ex.D-15, 16.
     
      
      . Dr. Ron Katznelson, plaintiffs’ expert, explained that a purchaser of a Dealer Demo chip or a Bag-O-Parts kit to descramble video additionally may extract the audio feed from a passing cable system, allowing the user receipt of descrambled video and audio portions of scrambled television programming without paying for the reception. Affidavit of Dr. Ron D. Katznel-son at 8. R5-146-8.
     
      
      . Kenny defined the phrase "break the VCII” as follows: "Break the VCII was any device that allowed one to either build a stand-alone VCII or make changes to the existing VCII which allowed somebody to get programming which they were not otherwise — they weren't entitled to." Deposition of Shaun Kenny at 201. Ex. B-201. Kenny further explained that he and Cooper “realized that the amount of money they [M/A-COM] were charging for the videocipher was going to only lead to piracy.... [b]ecause the price was too high, it was too lucrative. They made it too lucrative for someone to break it." Id. at 202.
     
      
      . Deposition of William S. Ward at 230. Ex.E-230.
     
      
      . Howes introduced the show as follows:
      This week we have the satellite television industry’s turkey of the year award going to the Videocipher II. What we’re going to be showing you is three methods currently available that are being marketed for breaking the audio on the VC-II.
      Boresight News Transcript at 1 (Dec. 4, 1986). R3-80-Ex.D-l.
     
      
      . Boresight News Transcript at 12 (Dec. 4, 1986). R3-80-Ex.D-12.
     
      
      . Boresight News Transcript at 21 (Dec. 11, 1986). R3-80-Ex.D-21.
     
      
      . The following Boresight excerpt, featuring Cooper in a segment entitled "Chips and Charlatans,” exemplifies the warnings of illegality given to viewers:
      Last week I suggested that if you were to buy a- chip you were doing at least two different things, two conscious acts, number one, number one it is illegal, it's illegal to use a chip to bust the VideoCipher encryption code. There are laws against such thing[s], there are fines and the jail terms are not insignificant if you are convicted of doing such a thing.
      Boresight News Transcript at 18 (Dec. 11, 1986). R3-80-Ex.D-18. See id. at 33, 44, 45, 52.
     
      
      . Kenny appealed to his Boresight audience for contributions to a legal defense fund as follows:
      [I]f you wanna fight and you wanna stand proud, and ... you wanna be able to look at yourself in the mirror, then stay up here and fight with us. It’s gonna cost you some bucks; might, you might have to go to court.... So this is the fighting ground right here, and the fighting right now requires some money. It’s gonna require alot of money. You may be one of the people that are sued.... Now, there is a trustee account that has been set up to stay here and fight this battle_ [C]ontri-bute to it. This is not gonna be a cheap fight_ [R]ight now we have to get ourselves positioned legally.
      Boresight News Transcript at 35-36 (Jan. 29, 1987). R3-80-Ex.D-35-36.
     
      
      . Boresight News Transcript at 4 (Dec. 4, 1986). R3-80-Ex.D-4. A Descrambling Summit advertisement, which appeared in the December, 1986 issue of Cooper’s publication stated that ”[s]ources for chips and hardware will be on hand prepared to ‘do business’ and establish distribution relationships so be prepared yourself to 'do business.’” Coop's Satellite Digest (Dec. 15, 1986). Ex.I-Ex.B.
     
      
      . Cooper explained the avoidance of American laws as the reason for locating the summit outside the United States as follows:
      This is not the United States. I'm going to say this for the record.... That means several things to you. It means that the laws and the rules and the regulations of this country are different from ... the United States_ So we can say things here. We can do things here. We can talk about things here that we simply couldn’t do in Ft. Lauderdale. I would not have hauled any of you from Ft. Lauder-dale down here if I thought we could have this kind of conference in Ft. Lauderdale. Descrambling Summit Transcript at 3 (Jan. 14, 1987). Ex.I-Ex.D-3.
     
      
      . Descrambling Summit Transcript at 50 (Jan. 14, 1987). Ex.I-Ex.D-50.
     
      
      . Descrambling Summit Transcript at 51-52 (Jan. 14, 1987). Ex.I-Ex.D-51-52.
     
      
      . Cable/Home Communications Corp. v. Heller, No. CIV 87-0017 PHX-CLH (D.Ariz. filed Jan. 7, 1987). Kenny purchased a pirate chip from a defendant in this lawsuit for $400.00.
     
      
      . In addition to defendants-appellants, the original complaint included former defendants Cooper, Howes and Bepko. Subsequently, former defendant Bepko and plaintiffs agreed to a final consent judgment and permanent injunction, and former defendant Howes was dismissed from the case by the district court pursuant to her settlement with plaintiffs. Former defendant Ward was added as a defendant in the second amended complaint, the operative complaint in this action. Ward was dismissed from the case pursuant to his entering into a final consent judgment and permanent injunction with plaintiffs. Although he remained a defendant in the case, Cooper has not appealed to this court.
     
      
      . Upon plaintiffs’ application for temporary amplification or modification of the preliminary injunction, the district court subsequently enlarged the preliminary injunction to require defendants to place all proceeds from a potential sale or transfer of any right or interest in Network in an interest-bearing escrow account identified to the court. Furthermore, defendants Network and Kenny were enjoined from removing their assets from the United States and concealing or encumbering their assets within the United States.
     
      
      .We note that the five orders appealed in this case are bare rulings without factual findings or legal conclusions by the district court. We recognize that Rule 52(a) of the Federal Rules of Civil Procedure states that findings of fact and conclusions of law are unnecessary for decisions on motions under Rules 12 and 56. Nevertheless, with particular regard to a grant of summary judgment, it is helpful to understand the reasoning of the district court.
     
      
      . Plaintiffs were represented by two law firms, one requesting a fee of $397,523.00 and costs of $8,338.07, and the other requesting a fee of $39,859.65 and costs of $6,068.34. Testimony at the evidentiary hearing revealed that the firms consciously avoided duplicating research time spent on the legal issues in the case. Furthermore, time for which the clients were billed, such as investigation of original claims, subsequently relinquished, settlement negotiations with other defendants, and communications with the United States Customs Service and the press, was deleted from plaintiffs’ requested fees. The magistrate found that plaintiffs’ explanatory testimony presented at the evidentiary hearing regarding attorneys’ fees and costs was unrebutted.
     
      
      . Following his review of the entire record from the perspective of the twelve guidelines in Johnson v. Georgia Highway Express, Inc., 488 F.2d 714, 717-19 (5th Cir.1974), the magistrate’s order explains his reasoning for the recommended award of attorneys’ fees and costs for the defendants’ copyright and communications violations:
      This is not Goliath taking revenge on David. Significantly, defendants utalized [sic] satellite broadcasts to reach viewers throughout the United States as well as international audiences. Defendants did not hesitate to solicit funds from their viewing audience in attempting to defend this lawsuit. Additionally, documentation exists in the record to demonstrate that a substantial number of persons attended the “Descrambling Summit” sponsored by defendants.
      This Court is impressed with the quality of pleadings it has reviewed and the meticulous documentation presented by plaintiffs in substantiation of the costs and fees sought. Plaintiffs’ expert was familiar with the record and offered credible testimony in support of plaintiffs’ applications for fees and costs. In contrast, defendants have not offered, and this Court is unable to locate, any evidence which demonstrates plaintiffs’ requests for fees and costs are unreasonable.
      Order at 6, 8 (Dec. 1, 1988) (footnote omitted) (magistrate’s order awarding attorneys’ fees and costs to plaintiffs). Supp. Rl-226-6, 8.
     
      
      . The Eleventh Circuit has adopted as precedent all decisions of the former Fifth Circuit rendered prior to October 1, 1981. Bonner v. City of Prichard, 661 F.2d 1206, 1207 (11th Cir.1981) (en banc).
     
      
      . In pertinent part, the Copyright Act confers the following exclusive rights on the copyright owner:
      Subject to sections 107 through 118, the owner of copyright under this title has the exclusive rights to do and to authorize any of the following:
      (1) to reproduce the copyrighted work in copies ...;
      (2) to prepare derivative works based upon the copyrighted work;
      (3) to distribute copies ... of the copyrighted work to the public by sale or other transfer of ownership, or by rental, lease, or lending....
      17 U.S.C. § 106 (1982). While these rights vest in the creator of an original work, the creator commonly sells them in exchange for services, such as production and marketing. See Harper & Row, Publishers, Inc. v. Nation Enterprises, 471 U.S. 539, 547, 105 S.Ct. 2218, 2223.
     
      
      . Computer programs are protected by the following provisions of the Copyright Act:
      A "computer program” is a set of statements or instructions to be used directly or indirectly in a computer in order to bring about a certain result.
      17 U.S.C. § 101 (1982).
      Copyright protection subsists, in accordance with this title, in original works of authorship fixed in any tangible medium of expression, now known or later developed, from which they can be perceived, reproduced, or otherwise communicated, either directly or with the aid of a machine or device.
      
        Id. at § 102(a).
     
      
      . In no case does copyright protection for an original work of authorship extend to any idea, procedure, process, system, method of operation, concept, principle, or discovery, regardless of the form in which it is described, explained, illustrated, or embodied in such work.
      17 U.S.C. § 102(b) (1982).
     
      
      . Franklin includes a thorough discussion of computer programming technology and legislative history of the 1980 amendments to the Copyright Act incorporating computer programs in its coverage. Because the Third Circuit instructively has explicated these areas, we will not duplicate that insightful exposition. Franklin, 714 F.2d at 1249-54.
     
      
      . There has been no issue in this case of the validity of M/A-COM's copyright for the CMS program within the U-30 chip contained in the VideoCipher®II, or of the Dealer Demo chip being an 86% copy of that CMS program, elements of a prima facie, copyright infringement case establishing copying. Donald Frederick Evans & Assocs., Inc. v. Continental Homes, Inc., 785 F.2d 897, 903 (11th Cir.1986); Original Appalachian Artworks, Inc. v. Toy Loft, Inc., 684 F.2d 821, 824 (11th Cir.1982); see 17 U.S.C. § 501 (1982); Sony, 464 U.S. at 433, 104 S.Ct. at 784. Defendants-appellants allege, however, that they were not aware that the CMS program within the U-30 chip was copyrighted. They apparently claim that the copyright notice inside the VideoCipher@II or on the CMS program was not evident. We note that a copyright notice on a compilation is sufficient; even a defective or omitted notice does not impair copyright protection under the Copyright Act. 17 U.S.C. § 405 (1982); Southern Bell Tel. & Tel. Co. v. Associated Tel. Directory Publishers, 756 F.2d 801, 811 (11th Cir.1985); Original Appalachian Artworks, 684 F.2d at 826-27; see also Tennessee Fabricating, 421 F.2d at 280-81 (Defendants were found to have infringed plaintiffs copyrighted architectural metal casting unit, although the unit that they used as a mold had the copyright notice obscured by paint.). While the notice was not apparent within the CMS computer program, it would have been obvious to anyone who removed the chip for the purpose of duplicating it in detail.
     
      
      . See, e.g., Columbia Pictures Indus., Inc. v. Aveco, Inc., 800 F.2d 59, 62 (3d Cir.1986) (Although defendant's customers actually placed the video cassette of copyrighted motion pictures in the video cassette player and operated the controls, defendant was liable for contributory infringement for renting rooms for this purpose.); Wales Indus. Inc. v. Hasbro Bradley, Inc., 612 F.Supp. 510, 518 (S.D.N.Y.1985) (Independent sales representatives, who advertised and promoted infringing products, may be held jointly and severally liable upon proof that they knew or should have known of the infringer's conduct whether or not they had any interest in or control over the infringer.); Screen Gems-Columbia Music, Inc. v. Mark-Fi Records, Inc., 256 F.Supp. 399, 404-05 (S.D.N.Y.1966) (Advertising agency, radio station that advertised the infringer's pirated records, and the packager that boxed and mailed the infringing records may all be held jointly and severally liable with the infringing manufacturer for copyright infringement if they knew or should have known of the infringement by such indications as a price suspiciously below the market price.).
     
      
      . Defendants-appellants have argued that they advertised and sold noninfringing products. For example, they contend that Kenny sold the Dealer Demo chip to satellite dish dealers for the purpose of demonstrating programming, that the installation of a socket in the slot containing the U-30 chip facilitated the insertion of a repair or diagnostic chip, and that the Bag-O-Parts kit was a device to "clean up” old video tapes, although they concede that these devices also decode the scrambled signals of the Video-Cipher®II. Appellants’ Brief at 15-19. While these alternative uses may be legitimate, we are not convinced that defendants-appellants used, promoted and sold these devices for any purpose other than to compromise the VideoCi-pher®II.
     
      
      . We note that granting summary judgment for contributory infringement has been upheld in cases with facts less compelling than the facts of this case. See, e.g., Redd Horne, 749 F.2d at 160-61 (affirming summary judgment for contributory infringement and permanent injunction against corporate defendant that advertised and promoted the infringing company’s renting video cassette viewing booths for viewing plaintiffs’ copyrighted films, despite imputed knowledge of infringing activities through defendant’s president who participated in the infringement and ignored plaintiffs' persistent requests that the infringing activity cease); Gershwin Publishing Corp., 443 F.2d at 1160-63 (affirming summary judgment for contributory infringement and permanent injunction against promoter that provided audiences for concerts in which performing artists infringed music copyrights).
     
      
      . The Comprehensive Cable Telecommunications Act of 1984, P.L. No. 98-549, 98 Stat. 2802 (1984 Cable Act), substantially amended and redesignated section 605 of the Federal Communications Act of 1934 as section 705. These amendments, however, are codified at 47 U.S.C. section 605. Through the amendments, Congress sought to address the problems created by the newly developed satellite cable technology. American Television & Communications Corp. v. Floken, Ltd., 629 F.Supp. 1462, 1468 (M.D.Fla.1986). The 1984 Cable Act preserves former section 605 virtually intact as subsection (a), and the amended section confirms the case law under the previous section. H.R.Rep. No. 934, 98th Cong., 2d Sess., reprinted in 1984 U.S.Code Cong. & Ad.News 4655, 4746; Floken, 629 F.Supp. at 1469.
     
      
      . In pertinent part, § 605(a) provides;
      No person not being entitled thereto shall receive or assist in receiving any interstate or foreign communication by radio and use such communication (or any information therein contained) for his own benefit or for the benefit of another not entitled thereto. No person having received any intercepted radio communication or having become acquainted with the contents, substance, purport, effect, or meaning of such communication (or any part thereof) knowing that such communication was intercepted, shall divulge or publish the existence, contents, substance, purport, effect, or meaning of such communication (or any part thereof) or use such communication (or any information therein contained) for his own benefit or for the benefit of another not entitled thereto.
      47 U.S.C. § 605(a) (Supp. V 1987).
     
      
      . The importation, manufacture, sale, or distribution of equipment by any person with the intent of its use to assist in any activity prohibited by subsection (a) of this section shall be subject to penalties and remedies under this subsection to the same extent and in the same manner as a person who has engaged in such prohibited activity.
      47 U.S.C. § 605(d)(4) (Supp. V 1987).
     
      
      . We are aware that the panel in this case vacated their opinion because of a settlement agreement between the parties. Showtime/The Movie Channel, Inc. v. Covered Bridge Condominium Ass’n, Inc., 895 F.2d 711 (11th Cir.1990) (per curiam). We, however, find the reasoning of the prior opinion most persuasive and applicable to the case before us. See Christianson v. Colt Indus. Operating Corp., 870 F.2d 1292, 1298 (7th Cir.), cert. denied, — U.S. -, 110 S.Ct. 81, 107 L.Ed.2d 87 (1989); Proffitt v. Wainwright, 685 F.2d 1227, 1266-67 (11th Cir.1982), cert. denied, 464 U.S. 1002, 104 S.Ct. 508, 78 L.Ed.2d 697 (1983).
     
      
      . [T]he term "encrypt”, when used with respect to satellite cable programming, means to transmit such programming in a form whereby the aural and visual characteristics (or both) are modified or altered for the purpose of preventing the unauthorized receipt of such programming by persons without authorized equipment which is designed to eliminate the effects of such modification or alteration ....
      47 U.S.C. § 605(c)(3) (Supp. V 1987).
     
      
      . In Johnson, the following considerations were found to be relevant to the determination of a reasonable attorneys’ fee award:
      1) the time and labor required;
      2) the novelty and difficulty of the questions;
      3) the skill requisite to perform the legal service properly;
      4) the preclusion of other employment by the attorney due to the acceptance of the case;
      5) the customary fee;
      6) whether the fee is fixed or contingent;
      7) time limitations imposed by the client or the circumstances;
      8) the amount involved and the results obtained;
      9) the experience, reputation and ability of the attorneys;
      10) the "undesirability” of the case;
      11) the nature and length of the professional relationship with the client; and
      12) awards in similar cases.
      
        Johnson, 488 F.2d at 717-19.
     
      
      . Defendants-appellants also have argued that the district court erred in failing to award only a proportionate share of the attorneys’ fees against Kenny and Network, since the suit originally was brought against four other defendants. Not only are we, as were the magistrate and district judge, impressed by plaintiffs-appel-lees’ deletions of time spent on original arguments not pursued and settlements with other defendants from their attorneys' fee request, but also this circuit has recognized that, in cases involving joint liability, counsel for prevailing parties often cannot account accurately for time spent litigating various issues with other defendants and unsuccessful claims, which may have been relevant to successful claims. See, e.g., Freeman v. Motor Convoy, Inc., 700 F.2d 1339, 1357 (11th Cir.1983) (In rejecting an analogous challenge to an attorneys’ fee award against a defendant employer solely for time spent litigating issues involving only defendant unions, this court agreed with the district court that “plaintiffs had already excluded, to the extent possible, the time spent on issues which only involved the defendant unions.”); Marion v. Barrier, 694 F.2d 229, 232 (11th Cir.1982) (per cu-riam) (Affirming an award of attorneys’ fees, this court acknowledged that “where evidence gathered in preparing an unsuccessful issue may also have been relevant to the successful claim, compensation should be provided for the time spent gathering that evidence.”); 2 M. Derf-ner & A. Wolf, Court Awarded Attorney Fees ¶ 17.03[2][a] n. 5.1 (1988) ("[Wjhere time spent on claims against a prevailing defendant also contributed to success against a dosing defendant, that time will be compensated by those defendants who have not escaped liability."); cf. Dean v. Gladney, 621 F.2d 1331, 1340 (5th Cir.1980) (Because the Fifth Circuit determined that the defendants were not joint tortfeasors, the case was remanded to the district court to “apportion the amounts of attorneys' fees owed to appellants by each of the officers.”), cert. denied, 450 U.S. 983, 101 S.Ct. 1521, 67 L.Ed.2d 819 (1981).
     
      
      . The applicable language of Rule 4(e) has been analyzed as follows in concluding that the state long-arm statute governs service in federal question cases, based on federal statutes, which do not contain a service of process provision:
      Whenever a statute or rule of court of the state in which the district court is held provides ... for service of a summons, or a notice, or of an order in lieu of summons upon a party not an inhabitant of or found within the state, ... service may ... be made under the circumstances and in the manner prescribed in the statute or rule.
      Fed.R.Civ.P. 4(e); Max Daetwyler Corp., 762 F.2d at 295-97; see Delong Equip. Co., 840 F.2d at 847; DeMelo, 711 F.2d at 1264-69. “Under the circumstances,” in the above-quoted second sentence of Rule 4(e), has been interpreted to mean amenability to service and consequent personal jurisdiction under the long-arm statute of the state in which the district court is located. Omni Capital Int’l, 484 U.S. at 105, 108 S.Ct. at 410; Max Daetwyler Corp., 762 F.2d at 295-96 n. 7; DeMelo, 711 F.2d at 1266; see Delong Equip. Co., 840 F.2d at 847; C. Wright & A. Miller, 
        Federal Practice & Procedure § 1075 at 494-96 (1987).
     
      
      . The Florida long-arm statute provides jurisdiction for the commission of a tortious act within the state as follows:
      (1) Any person, whether or not a citizen or resident of this state, who personally or through an agent does any of the acts enumerated in this subsection thereby submits himself and, if he is a natural person, his personal representative to the jurisdiction of the courts of this state for any cause of action arising from the doing of any of the following acts:
      (b) Committing a tortious act within this state.
      Fla.Stat. § 48.193(l)(b).
     
      
      . "Specific jurisdiction" is the exercise of personal jurisdiction over a nonresident defendant by a forum "arising out of or related to the defendant’s contacts with the forum.” Helicopteros Nacionales de Colombia, S.A. v. Hall, 466 U.S. 408. 414 n. 8. 104 S.Ct. 1868, 1872 n. 8 (1984). "General jurisdiction" is the exercise of personal jurisdiction over a nonresident defendant by a forum "not arising out of or related to the defendant’s contacts with the forum.” 466 U.S. at 414 n. 9, 104 S.Ct. at 1872 n. 9.
     