
    UNITED STATES of America, Appellee, v. Christopher MOORE, Defendant-Appellant.
    No. 790, Docket 94-1330.
    United States Court of Appeals, Second Circuit.
    Argued Jan. 10, 1995.
    Decided April 25, 1995.
    
      J. Bruce Maffeo, Bernstein & Maffeo, New York City (Michele C. Cacioppo, Bernstein & Maffeo, New York City, of counsel), for defendant-appellant.
    Leonard Lato, Asst. U.S. Atty., Brooklyn, NY (Emily Berger, Asst. U.S. Atty., Brooklyn, NY, and Zachary W. Carter, U.S. Atty., Brooklyn, NY, of counsel), for appellee.
    Before: KEARSE, McLAUGHLIN, and PARKER, Circuit Judges.
   McLAUGHLIN, Circuit Judge:

Christopher Moore was indicted on nine drug-related counts: conspiracy to distribute cocaine base (“crack cocaine”), in violation of 21 U.S.C. §§ 846, 841(b)(1)(A) (count one); distribution and possession with intent to distribute cocaine base, in violation of 21 U.S.C. §§ 841(a)(1), 841(b)(1)(C), on August 30, 1991 (count two), on September 13, 1991 (count three), and on November 7, 1991 (count four); intentional use and carrying of firearms during and in relation to the drug conspiracy, in violation of 18 U.S.C. § 924(c)(1) (count five (a) through five (k)) (11 subcounts, each involving a different firearm) (“drug-related firearms count”); and possession of firearms with the manufacturer’s serial number removed and obliterated, in violation of 18 U.S.C. §§ 922(k), 924(a)(1) (counts six through nine) (“defaced serial numbers counts”).

Following a jury trial, in the United States District for the Eastern District of New York (Charles P. Sifton, Chief Judge), Moore was found guilty on counts one, two, four, five, seven and nine. He was acquitted of counts three, six and eight. The court sentenced him to a prison term of life on count one, 20 years on counts two and four, five years on counts seven and nine, all of which run concurrently, and to a consecutive term of five years on count five. In addition, Moore received fines of $1 million on counts one, two and four, and $250,000 on counts five, seven and nine, all of which were imposed concurrently.

On appeal, Moore’s most compelling argument is that the 100 to 1 sentencing ratio contained in 21 U.S.C. § 841(b) and U.S.S.G. § 2D1.1 (which equates the offense levels of 100 grams of powder cocaine and 1 gram of crack cocaine) violates equal protection. This Court has already held that the sentencing scheme does not violate equal protection under a rational basis review. United States v. Stevens, 19 F.3d 93 (2d Cir.1994). Moore now mounts an equal protection challenge to the sentencing scheme, arguing that Congress acted with a discriminatory purpose.

Moore also appeals his conviction, contending that: (1) the district court abused its discretion by denying his motion for a new trial based on newly discovered evidence that two police officers committed perjury; and (2) there was insufficient evidence to convict on the firearms counts. Moore further appeals his sentence, arguing that: (1) the district court erred in estimating the amount of drugs distributed by Moore; and (2) the district court failed to consider a downward departure. We affirm both the conviction and the sentence.

BACKGROUND

Moore’s distribution network

Defendant was the leader of a local crack distribution organization that operated in Brooklyn, and included, among others, Michelle Ruiz, Daniel Gladden (“Raz” or “Noodles”), an individual named Anthony (“Ant”), Bobby Myrick, David Frasier (“Crackhead Dave”), Edward Davis, James Kimball, William Jiminez, and Timothy Cyrus. Moore organized a division of labor within the network, and maintained discipline through violence and intimidation. Some members, e.g., Ruiz, specialized in preparing, cutting up and packaging the crack cocaine. Others, known as “runners,” such as Gladden, transferred the processed, ready-for-sale crack cocaine to the most visible members of the organization, the “street sellers,” and simultaneously collected the proceeds from them. The street sellers worked two locations near Moore’s lingerie store and his barber shop. The organization also used various locations — e.g., 523 Euclid Avenue, 1018 Belmont Avenue, and 474 Pine Street — as “stash houses” to store and process contraband. Additionally, Moore supplied several network members with guns.

Police Investigation

In August 1991, police officers Robert Sehulman and Brian Lavin began surveilling Moore and his organization. From a variety of locations, the officers observed the daily exchange of vials containing a white rock-like substance for money. They saw Moore direct and receive currency from the street dealers. For example, they overheard Moore order sellers “to be more careful of his product” and “keep an eye out for cops.” They further noted that, with few exceptions, the only people who entered the lingerie store were members of the organization, the store had no set hours, and it was open as late as 3:00 a.m.

Starting in late August 1991, Sehulman and Lavin made a series of arrests and seizures of contraband that would culminate in the arrest of Moore: on August 24, they arrested Jiminez selling crack cocaine near the lingerie store, and seized several vials that contained crack; on August 30, they arrested Davis selling crack cocaine in the lot behind the lingerie store, seized a loaded Smith and Wesson .357 magnum that Davis had dropped, and, after pursuing another seller (who got away) into the basement of the lingerie store, they recovered a police scanner, money and vials containing a white, rock-like substance; on September 13, they seized 12 crack vials, but Cyrus and Myrick escaped; on October 15, they arrested Myr-ick and Frasier; on November 7, they arrested Cyrus and Kimble; and on February 5, 1992, police officer Vincente DeQueiroz, entered the apartment at 523 Euclid Avenue, arrested Cyrus, Luis Valentine, and Benjamin Colon, and seized 267 vials of crack.

In February 1992, the police executed a number of search warrants. They seized from Ruiz’s home two guns (a Davis .380 semiautomatic pistol and a Gloek .45-caliber pistol) with the serial numbers obliterated. The biggest seizures occurred across the street from the lingerie store at 1018 Belmont Ave and 474 Pine Street: the police seized an arsenal of weapons; documents upon which were written the words “Ant,” “Nud,” and “Nudles” (aliases of organization members); and vials containing a white rock-like substance. Shortly thereafter, Moore was arrested and indicted.

Evidence at trial

At trial, two trusted members of Moore’s network, cooperating witnesses Ruiz and Gladden, testified against Moore. Ruiz implicated Moore as the head of the distribution network, and described the workings of the organization. Ruiz explained that, in May 1991, Moore taught her how to cut and package crack, and recruited her for his organization. Ruiz testified that she prepared crack two to three times per week, and was paid around $400 per job (about 800 packaged vials). There was testimony that each vial contained approximately .07 grams of crack. Occasionally, she was not paid in money; for example, once Moore paid her with a Davis .380 semi-automatic weapon, which she put in a drawer in her apartment. Ruiz also testified that, while Moore was in her apartment, Gladden brought to Moore a Glock .45 semiautomatic pistol in a brown paper bag. Moore then gave the brown paper bag containing the pistol to Ruiz. Ruiz put the gun in her bureau. Both guns remained there until the police seized them. Ruiz worked full-time for Moore’s organization for about one year.

Both Ruiz and Gladden testified as to Moore’s violence. When Ruiz initially refused to join the organization, Moore drove her to a Burger King parking lot and “show[ed] who he really is.” He dragged her by, the hair, slapped her and beat her. Moore’s attention similarly extended to other members of his network. For example, later that night, he and Ruiz met David “Crackhead Dave” Frasier at the lingerie store. After excoriating Crackhead Dave for “fuek[ing] up,” Moore ordered others to beat him. While Dave was being viciously beaten and Ruiz was crying, Moore warned her that she would suffer the same fate if she did not obey him. Gladden similarly related that Moore ordered dealers who “came up short” to be beaten.

Gladden corroborated much of Ruiz’ testimony. Although he worked mostly as a runner, Gladden occasionally doubled as a street seller, where he sold approximately 460 five-dollar vials per day (gross daily sales of around $2,300). Gladden testified that Davis’ Smith & Wesson .357 magnum (seized by Schulman and Lavin) was an “organization gun” that Moore had loaned to Gladden previously.

Officers Schulman and Lavin similarly testified to an extensive, ongoing crack-distribution network headed by Moore. Their testimony was accompanied by videotapes of various organization members, including Timothy Cyrus, engaged in street sales of crack cocaine. The officers made the videotapes in January, 1992.

At the close of the case, Moore moved for a judgment of acquittal on counts two, three and five. The court reserved decision, and subsequently denied the motion after the jury rendered its verdict.

Moore was convicted of conspiracy to distribute crack cocaine; distribution and possession with intent to distribute crack cocaine on August 30, 1991 and November 7, 1991; the drug-related firearms count; and two of the defaced firearms counts (the Glock .45 and the Davis .380 semiautomatic pistols seized from Ruiz’ apartment).

Post-trial proceedings

Moore first moved to set aside the jury’s verdict solely on the drug-related firearms count. The district court denied the motion. Moore then moved, pro se for a new trial (counsel remained in an advisory role), which was denied summarily. Later, Moore moved for a new trial based on allegedly newly discovered evidence that officers Lavin and Schulman perjured themselves. The district court again denied the motion. Moore then moved for reconsideration of the perjury motion, focusing on a different alleged perjury by the police officers. Once again, the district court denied the motion.

Additionally, in several pre-sentencing memoranda, Moore challenged the constitutionality of the 100 grams of powder cocaine equals 1 gram of crack cocaine sentencing ratio contained in 21 U.S.C. § 841(b) and U.S.S.G. § 2D1.1. Moore also argued that the amount of drugs attributable to him was highly inflated, and, alternatively, that the district court should depart downwardly to prevent an injustice. The district court agreed with Moore that the government’s calculation of his base offense level was too high, settled on a middle ground, then denied his remaining sentencing applications.

The court sentenced Moore, as noted above. Moore now appeals.

DISCUSSION

1. Equal Protection.

An intentionally discriminatory classification imposed by federal law violates the equal protection component of the Fifth Amendment’s due process clause. See Washington v. Davis, 426 U.S. 229, 239, 96 S.Ct. 2040, 2047, 48 L.Ed.2d 597 (1976); Bolling v. Sharpe, 347 U.S. 497, 499-500, 74 S.Ct. 693, 694-95, 98 L.Ed. 884 (1954). Moore argues that 21 U.S.C. § 841(b)(1) and U.S.S.G. § 2D1.1 violate equal protection because they incorporate a 100 to 1 sentencing ratio of powder cocaine to crack cocaine. He contends that, when Congress enacted the differential ratio, it intended to discriminate against Blacks, i.e., it had a racially discriminatory purpose. We disagree.

When assailing legislation that, on its face, is not racially discriminatory, two lines of attack are generally available to raise an equal protection claim: the distinguishing feature is the presence of an allegation of discriminatory intent. If the plaintiffs do not allege actual discriminatory intent, the deferential “rational basis” standard is used to review the challenged legislative scheme. See Rogers v. Lodge, 458 U.S. 613, 617 & n. 5, 102 S.Ct. 3272, 3275 & n. 5, 73 L.Ed.2d 1012 (1982); Village of Arlington Heights v. Metropolitan Hous. Dev., 429 U.S. 252, 265-66, 97 S.Ct. 555, 563-64, 50 L.Ed.2d 450 (1977); United States v. Stevens, 19 F.3d 93, 96 (2d Cir.1994). If, on the other hand, plaintiffs allege and demonstrate that the legislators passed the law with a discriminatory purpose, courts then review the challenged legislation under the demanding “strict scrutiny” standard. See Rogers, 458 U.S. at 617 & n. 5, 102 S.Ct. at 3275 & n. 5; Washington, 426 U.S. at 242, 247-48, 96 S.Ct. at 2049, 2051-52; United States v. Singleter ry, 29 F.3d 733, 741 (1st Cir.), cert. denied, — U.S. —, 115 S.Ct. 647, 130 L.Ed.2d 552 (1994).

In United States v. Stevens, we recently held that a rational basis exists for Congress’ establishment of the 100 to 1 sentencing ratio:

Congress had a valid reason for mandating harsher penalties for crack as opposed to powder cocaine: the greater accessibility and addictiveness of crack. Because we believe that treatment of one gram of crack cocaine as the equivalent of 100 grams of powder cocaine is rationally related to the legitimate governmental purpose of protecting the public against the greater dangers of crack cocaine, we reject [appellant’s] equal protection challenge to this sentencing scheme.

Stevens, 19 F.3d at 97 (citations omitted). The Stevens court expressly declined to subject the legislation to stricter judicial scrutiny, noting that appellant did not “contend that either Congress or the Federal Sentencing Commission acted with discriminatory intent.” Id. at 96. Moore now presses that claim.

Because discriminatory intent rarely is susceptible of direct proof, litigants may make “a sensitive inquiry into such circumstantial and direct evidence of intent as may be available.” Village of Arlington Heights, 429 U.S. at 266-68, 97 S.Ct. at 563-65 (“Sometimes a clear pattern, unexplainable on grounds other than race, emerges from the effect of the state action even when the governing legislation appears neutral on its face.... The historical background of the decision is one evidentiary source.... The legislative or administrative history may [also] be highly relevant_”). Additionally, discriminatory purpose “implies that the de-cisionmaker, in this ease [Congress], selected or reaffirmed a particular course of action at least in part ‘because of,’ not merely ‘in spite of,’ its adverse effects upon an identifiable group.” Personnel Adm’r v. Feeney, 442 U.S. 256, 279, 99 S.Ct. 2282, 2296, 60 L.Ed.2d 870 (1979).

Moore is not the first defendant to charge Congress and the Sentencing Commission with discriminatory intent in establishing the 100 (powder) to 1 (crack) ratio. Every circuit court that has addressed this issue has held that there is no evidence of a racially discriminatory purpose behind the ratio. See United States v. Clary, 34 F.3d 709, 713 (8th Cir.1994), cert. denied, — U.S. —, 115 S.Ct. 1172, 130 L.Ed.2d 1126 (1995); Singleterry, 29. F.3d at 741; United States v. Byse, 28 F.3d 1165, 1169 (11th Cir.1994), cert. denied, — U.S. —, 115 S.Ct. 767, 130 L.Ed.2d 663 (1995); United States v. Thurmond, 7 F.3d 947, 950-53 (10th Cir.1993), cert. denied, — U.S. —, 114 S.Ct. 1311, 127 L.Ed.2d 661 (1994); United States v. Reece, 994 F.2d 277, 278-79 (6th Cir.1993) (per curiam); United States v. Frazier, 981 F.2d 92, 95 (3d Cir.1992) (per curiam), cert. denied, — U.S. —, 113 S.Ct. 1661, 123 L.Ed.2d 279 (1993); United States v. Galloway, 951 F.2d 64, 65-66 (5th Cir.1992) (per curiam). See also United States v. Jackson, 856 F.Supp. 176, 177 (S.D.N.Y.1994); United States v. Walls, 841 F.Supp. 24, 31 (D.D.C.1994).

Notwithstanding the overwhelming weight of authority against him, Moore contends that the statistical evidence of disparate impact, when analyzed with the legislative record and the superficiality of Congress’ inquiry, compels the conclusion that Congress acted with a discriminatory purpose.

The statistical evidence regarding discriminatory impact is, indeed, irresistible: approximately 88% of defendants charged with crack cocaine-related crimes are Black (the percentage is even higher in some urban areas). See United States Sentencing Commission, Special Report to Congress: Cocaine and Federal Sentencing Policy, at 156 (February 1995). To support his charge that the passage of the 1986 Act was “shot through with racial references, many of them overt,” Moore cites the congressional testimony of a Florida sheriff who describes the “typical” crack dealer as “ ‘a big-shouldered Trinidadian wearing gold chains and a diamond-studded bracelet.’ ” Walls, 841 F.Supp. at 28 (quoting 132 Cong.Rec. S7123-25 (daily ed. June 9, 1986)). He also cites the following passage that, he argues, captured the tone of the congressional debate:

Street sales of cocaine rocks [crack cocaine] have occurred in the same neighborhoods where other drugs were sold in the past: run-down, black neighborhoods from Delray Beach to Fort Pierce. But the drug market is also creeping into other neighborhoods.
An interracial neighborhood east of Howard Park has become one of West Palm Beach’s most highly visible cocaine rock areas. Less than a block from where unsuspecting white retirees play tennis, gangs of young black men push their rocks on passing motorists, interested or not.

132 Cong.Rec. S4668 (daily ed. April 22, 1986) (emphasis added). Other courts have cited language from the congressional hearings and debates that similarly raises the judicial eyebrow. See, e.g., United States v. Clary, 846 F.Supp. 768, 783-84 & nn. 48-50 (E.D.Mo.) rev’d, 34 F.3d 709 (8th Cir.1994), cert. denied, — U.S. —, 115 S.Ct. 1172, 130 L.Ed.2d 1126 (1995).

Moore further notes as evidence of discriminatory intent that the bill was rushed through Congress without meaningful deliberation. He explains that: (1) a relatively short time was allotted to debate the bill; (2) the 100 to 1 ratio was “arbitrarily doubled [from 50 to 1] simply to symbolize redoubled congressional seriousness,” Walls, 841 F.Supp. at 29-30 (quoting testimony of Eric Sterling, former staff counsel to the House Subcommittee on Crime); and (3) the stated justification for the increased penalties — the greater addictiveness of crack — has been discredited by the medical establishment.

Although Moore’s arguments are compelling, we are not persuaded. A careful analysis of the legislative history and background regarding the 100 to 1 ratio demonstrates Congress enacted the sentencing ratio for a valid, stated purpose. See Stevens, 19 F.3d at 97 (“the greater accessibility and addie-tiveness of crack”). Other courts that have conducted similarly thorough reviews have come to the same conclusion. See, e.g., Thurmond, 7 F.3d at 953 (citing statements from congressional hearings and concluding that Congress imposed the 100 to 1 ratio because crack cocaine “(1) has a more rapid onset of action, (2) is more potent, (3) is more highly addictive, (4) is less expensive than cocaine powder, and (5) has widespread availability”); United States v. Buckner, 894 F.2d 975, 978-79 & nn. 9-10 (8th Cir.1990) (extensive analysis and quotations from congressional hearings on crack cocaine concerning its potency, addictive nature, and prevalence); Singleterry, 29 F.3d at 741 (“[T]here are racially neutral grounds for the classification that more plausibly explain its impact on blacks. As a result, there is insufficient evidence that the distinction drawn between [crack] and cocaine was motivated by any racial animus or discriminatory intent.”) (quotations omitted); Walls, 841 F.Supp. at 31 (concluding after a close examination of the legislative history along the lines which Moore suggests that “[t]he racial implications of the legislative history of the [statute] are too sparse, too tangential, or too remote in time to support a finding that a majority in Congress in 1986 intended the crack penalties to discriminate against blacks.”).

Moore concedes in his reply brief that United States v. Clary, 846 F.Supp. 768 (E.D.Mo.1994), the only case Moore cites where a federal court found that the 100 to 1 ratio violated equal protection, was reversed by the Eighth Circuit. See Clary, 34 F.3d at 714. Shepherding the Eighth Circuit into the fold, the Clary court concluded that the quoted legislative history merely evinced a “racial consciousness” that was proper for Congress to consider in its debate, and fell short of proving an improper “racial animus.” Id. at 713-14 (“It is too long a leap from newspaper and magazine articles [placed in the Congressional Record] to an inference that Congress enacted the crack statute because of its adverse effect on African American males, instead of the stated purpose of responding to the serious impact of a rapidly-developing and partieularly-dangerous form of drug use.”).

We are not moved by Moore’s arguments about the haste with which the bill went through Congress and the lack of meaningful deliberation. Those considerations bear more heavily on the issue of the legislative scheme’s arbitrariness and rationality, than the issue of purposeful discrimination. In any event, the Clary court offered a racially neutral reason why Congress enacted the legislation without much debate: Congress was in agreement that the burgeoning crack epidemic was a serious problem that had to be addressed quickly by harsh penalties. Id. at 713.

Furthermore, it is irrelevant whether the medical establishment has discredited the greater addictiveness of crack cocaine because “[s]cientific disagreement with testimony in congressional hearings, offered at a later time and after additional research, simply does not establish discriminatory purpose, or for that matter, a lack of scientific support for Congress’ action.” Id. at 714. Moreover, this reason was never the sole rationale justifying the 100 to 1 ratio.

Finally, we are not unmindful that the Sentencing Commission’s Special Report to Congress regarding Cocaine and Federal Sentencing Policy has recently concluded that Congress should revisit the 100 to 1 sentencing ratio. The report does not change our analysis. Importantly, it does not conclude there was any intentional discrimination by Congress. Similarly, adverse media attention, see, e.g., Cocaine Injustice, N.Y. Times, Mar. 9, 1995, at A24, as well as the plethora of similar lawsuits challenging the 100 to 1 sentencing ratio throughout the nation, do not affect our analysis of Congress’ intent in 1986.

We conclude that Congress and the Sentencing Commission did not enact the 100 to 1 ratio with a discriminatory intent, and, therefore, reject defendant’s contention that we should invalidate the legislation on equal protection grounds.

2. Newly Discovered Evidence of Perjury of Schulman and Lavin.

Moore argues that the district court abused its discretion by denying Moore’s motion for a new trial based on newly discovered evidence that the two police officers, Schulman and Lavin, committed perjury. We disagree.

We review motions for a new trial with caution, and grant them only in extraordinary circumstances. See United States v. Spencer, 4 F.3d 115, 118 (2d Cir.1993); United States v. Sanchez, 969 F.2d 1409, 1414 (2d Cir.1992). These motions are appropriately committed to the trial court’s discretion, see Sanchez, 969 F.2d at 1413, and we will not overturn that decision in. the absence of abuse. United States v. Parker, 903 F.2d 91, 103 (2d Cir.1990).

When a motion for a new trial rests on newly discovered evidence, defendants must show the trial court that, with due diligence, they could not have discovered the evidence during trial. United States v. Siddiqi, 959 F.2d 1167, 1173 (2d Cir.1992); Sanders v. Sullivan, 863 F.2d 218, 226 (2d Cir.1988). The evidence must also be material, see United States v. Wallach, 935 F.2d 445, 456 (2d Cir.1991), cert. denied, — U.S. —, 113 S.Ct. 2414, 124 L.Ed.2d 637 (1993), and noncumulative. See United States v. Petrillo, 821 F.2d 85, 90 (2d Cir.1987).

When alleged perjury is involved, not only must defendant demónstrate that the witness committed perjury, see United States v. White, 972 F.2d 16, 20 (2d Cir.), cert. denied, — U.S. —, 113 S.Ct. 669, 121 L.Ed.2d 593 (1992), but also “that the jury probably would have acquitted in the absence of the false testimony.” Sanchez, 969 F.2d at 1413-14; see United States v. Stofsky, 527 F.2d 237, 245-46 (2d Cir.1975), cert. denied, 429 U.S. 819, 97 S.Ct. 65, 50 L.Ed.2d 80 (1976).

Moore fails to sustain his heavy burden. The gravamen of Moore’s. allegation is that Schulman and Lavin perjured themselves when they testified that Timothy Cyrus was not a government informant at the time they videotaped him peddling crack for the organization. Moore claims that Timothy Cyrus actually began cooperating with the police shortly after his arrest on November 7, 1991, not the last week in January 1992, as the government contends.

. Characterizing the videotape as the “centerpiece” of the government’s case at trial, Moore argues that it infected the jury’s determination of guilt, and directly bore on Moore’s trial defense that Schulman and La-vin manufactured a case against him in retaliation for Moore’s charges of theft and an illegal search against Lavin in August 1991. (In August 1991, after Davis’ arrest, Moore filed a complaint with the Police Department’s Internal Affairs Bureau (“LAB”) against Lavin for stealing money and conducting an illegal search of Moore’s lingerie store. LAB concluded that Lavin had conducted an illegal search, but found the theft claim unsubstantiated.)

Moore learned of the alleged perjury only during a fortuitous post-trial conversation with Timothy Cyrus’ counsel in a separate proceeding. Moore argues that Schulman’s and Lavin’s grand jury testimony indicated that Cyrus began cooperating shortly after his November 7 arrest, in contrast to their testimony at trial. Moore further claims that two DEA reports prepared by Special Agent Pinnock refer to debriefings of Timothy Cyrus that occurred on January 14, 1992, four days before Cyrus was videotaped. Finally, Moore contends that the absence of any note about Cyrus’ November 7, 1991 arrest in Cyrus’ arrest record confirms that Cyrus had begun cooperating shortly after his arrest on November 7.

A careful review of the record reveals that Timothy Cyrus had not begun cooperating until late January. As to the DEA reports, Agent Pinnock stated in a post-trial affidavit that the reports referred to two different people, “Debriefing of SCT-92-0021” referred to Andrew Cyrus, and “Debriefing of a Confidential Source of Information,” referred to Timothy Cyrus. The two debriefings occurred on different days and in different locations. Andrew’s debriefing occurred on January 14, 1992. In his sworn affidavit, Pinnock stated that the date of Timothy’s debriefing written on the document, also January 14, was incorrect. In fact, the report refers to Timothy’s observation of Moore cooking crack on January 16, two days after the date on the document.

Regarding the November 7 arrest, the record shows that Cyrus was processed like any non-cooperating individual. For example, he remained in custody until November 13, and was released then only because the prosecutor had failed to file a felony indictment within the time required by law. He was later indicted, and had an active case file as late as January 27, 1992. Moreover, Cyrus’ attorney stated that he was still engaged in ongoing discussions concerning Cyrus’ cooperation until January 25, suggesting that any cooperation agreement had not been formalized by then.

As to the grand jury testimony of Schul-man and Lavin, we find no inconsistency that rises to the level of perjury. Specifically, at the grand jury, Schulman merely answered “yes” after being asked whether Timothy Cyrus agreed to cooperate after his arrest— a true statement since Schulman gave no time referent. Additionally, at trial, Schul-man merely confused Timothy Cyrus with Andrew Cyrus during a brief line of questioning.

Moore’s other claims of newly discovered evidence are meritless and were adequately disposed of by the district court’s memorandum decision. See United States v. Moore, CR-92-0200 (CPS) (S.D.N.Y. Jan. 12, 1992). Accordingly, the district court did not abuse its discretion in denying Moore’s motion for a new trial.

3. Sufficiency of the Evidence.

Moore argues that there was insufficient evidence to convict on the drug-related firearms count and the defaced serial numbers counts. Moore’s argument lacks merit.

Defendant bears a heavy burden when challenging the sufficiency of evidence. United States v. Sureff 15 F.3d 225, 228 (2d Cir.1994). The evidence must be viewed in the light most favorable to the government, see United States v. Amato, 15 F.3d 230, 235 (2d Cir.1994), and all permissible inferences and issues of credibility must be drawn in the government’s favor. United States v. Torres, 901 F.2d 205, 216 (2d Cir.), cert. denied, 498 U.S. 906, 111 S.Ct. 273, 112 L.Ed.2d 229 (1990). The conviction must stand if any rational trier of fact could have found the essential elements of the crime established beyond a reasonable doubt. Amato, 15 F.3d at 235. The jury may properly reach its verdict based upon inferences drawn irom circumstantial evidence, United States v. Mariani, 725 F.2d 862, 865-66 (2d Cir.1984), and pieces of evidence must be viewed in conjunction, not in isolation. See United States v. Podlog, 35 F.3d 699, 705 (2d Cir.1994), cert. denied, — U.S. —, 115 S.Ct. 954, 130 L.Ed.2d 897 (1995).

We need not tarry long with the substantive sufficiency of the evidence. The drug-related firearms count contained three sub-counts — count 5(e) (Glock .45-caliber semiautomatic pistol), count 5(h) (Davis .380 semiautomatic pistol), and count 5(j) (Smith & Wesson .357 Magnum) — upon which the jury found Moore guilty. Because each subcount contained a different weapon that Moore used to further the conspiracy, the jury need only have found Moore guilty on any one of the subcounts in order to convict on the single drug-related firearms count.

To sustain the conviction on the drug related firearms count, the government must show that: (1) the defendant used or carried a firearm; and (2) the use or carrying was during and in relation to a drug trafficking ciime. See Smith v. United States, — U.S. —, —, 113 S.Ct. 2050, 2053, 124 L.Ed.2d 138 (1993); United States v. Santeramo, 45 F.3d 622, 623 (2d Cir.1995). In Smith, the Supreme Court held that attempting to trade a firearm for narcotics was a “use” of a firearm within the meaning of the statute. It explained that “[b]y attempting to trade his [firearm] for the drugs, [defendant] ‘used’ or ‘employed’ it as an item of barter to obtain cocaine; he ‘derived service’ from it because it was going to bring him the very drugs he sought.” Smith, — U.S. at —, 113 S.Ct. at 2054. Further, it clarified that the phrase “during and in relation to” meant that “the gun at least must ‘facilitate], or ha[ve] the potential of facilitating,’ the drug trafficking offense.” Id. at —, 113 S.Ct. at 2059 (citations omitted).

Count 5(h) concerned the Davis .380 semiautomatic pistol that Moore had given Ruiz as partial payment for her drug-related services. It falls squarely under Smith. By trading the gun for Ruiz’ drug-related services, Moore used it as an item of barter and “derived service” from the gun in furtherance of the drug conspiracy. The gun facilitated the drug distribution conspiracy because it was used as compensation for drug services rendered, and as an incentive for Ruiz to continue her involvement in the conspiracy. Therefore, the evidence presented was sufficient to convict.

We additionally find meritless Moore’s arguments regarding the two other subcounts. Accordingly, there was sufficient evidence to convict Moore on the drug-related firearms count.

Regarding the defaced firearms counts, the government must prove that the defendant knowingly possessed a firearm with an obliterated serial number. See 18 U.S.C. § 922(k). The defendant must know that the firearm had an altered serial number. See United States v. Haynes, 16 F.3d 29, 34 (2d Cir.1994); United States v. Hooker, 997 F.2d 67, 72 (5th Cir.1993). Moore contends that the government failed to prove that Moore had the requisite knowledge when he gave Ruiz the guns because the record contains no testimony that Moore knew the serial numbers were obliterated.

Police seized the guns in these two counts — counts seven (Glock .45 semiautomatic pistol) and nine (Davis .380 semiautomatic pistol) — at Ruiz’ apartment. Trial testimony established that Gladden brought the Glock .45 to Ruiz’ apartment in a brown paper bag and gave it to Moore, who then gave it to Ruiz. Ruiz put the gun in the bureau without looking at it. Similarly, Moore gave Ruiz the Davis .380, and she put it in her drawer. Both guns remained there until the police seized them. Given such testimony, a rational juror could conclude that the serial numbers on the guns had been removed before Ruiz received them. A rational juror could also conclude that when Moore distributed guns to members of the organization he had inspected them and was aware that they lacked serial numbers. Moore’s sufficiency challenge regarding the defaced firearms counts is therefore unavailing.

4. Calculation of the Quantity of Drugs Attributable to Moore.

Moore contends that the district court incorrectly estimated the amount of drugs in its Guideline computation because “the government offered only the flimsiest testimony in support of the quantity of drugs involved and the length of the conspiracy.” Moore’s argument lacks merit.

A district court’s estimation of drug quantity is an issue of fact that need be established only by a preponderance of the evidence. See United States v. Wilson, 11 F.3d 346, 355 (2d Cir.1993), cert. denied, — U.S. —, 114 S.Ct. 2142, 128 L.Ed.2d 870 (1994). In Moore’s case, however, the district court charitably employed the more rigorous “clear and convincing” standard to Moore’s benefit.

The government argued Moore should be sentenced for distributing between 5 to 15 kilograms (base offense level 40) because: (1) Ruiz packaged approximately 800 vials of crack (.07 grams per vial) two to three times per week for about one year (between approximately 5.5 and 8 kilos); and (2) Ruiz’ and Gladden’s testimony established that the organization packaged and distributed well over 100 grams of crack per week for about one year. Moore, on the other hand, argues that he should be sentenced based on the much lower amount of drugs that police had seized or that Moore was actually convicted of possessing.

Tellingly, the district court accepted neither formulation, choosing, instead, a middle ground. See United States v. Colon, 961 F.2d 41, 43 (2d Cir.1992) (where police seized only 149 envelopes each containing .05 grams of heroin and testimony established that defendant sold 80 similar envelopes every two or three days for a few years, sentencing court correctly approximated the drug quantity conservatively estimating sales at 80 envelopes every three days for one year). The district court decided on a calculation of 800 vials twice per week for a year with reasonable deductions for losses and disruptions in the organization. Thus, the court’s final determination of the drugs attributable to Moore — between 1.5 to 5 kilograms — was carefully considered, conservative, and based on the evidence presented, primarily Ruiz’ and Gladden’s testimony. Accordingly, the court did not err in estimating the amount of drugs in its determination of the base offense level.

5. Downward Departure from the Guidelines.

Moore’s final contention is that the district court failed to consider his application for a downward departure. Once again, we disagree.

Defendants may appeal a district court’s determination that it lacked authority to depart from the guidelines. See United States v. Speenburgh, 990 F.2d 72, 75 (2d Cir.1993). A discretionary refusal to depart, however, is not appealable. United States v. Lawal, 17 F.3d 560, 562-63 (2d Cir.1994); United States v. Califano, 978 F.2d 65, 65 (2d Cir.1992).

We find nothing in the record suggesting that the district court mistakenly believed it had no authority to depart downwardly. We have previously stated that “a district court’s silence concerning its refusal to depart downward does not support an inference that the district court misapprehended its scope of authority.” Lawal, 17 F.3d at 563. In any event, Moore’s judgment of sentence expressly stated that the court “f[ound] no reason to depart from the sentence called for by application of the guidelines.” Accordingly, we reject Moore’s contention that the district court mistakenly believed that it lacked the authority to depart downwardly.

CONCLUSION

The statistical evidence of disparate impact and several questionable passages in the legislative record are discomfitting. Moore’s arguments raise troublesome questions about the fairness of the crack cocaine sentencing policy. Although we conclude that neither Congress nor the Sentencing Commission acted with discriminatory purpose when they established the 100 to 1 sentencing ratio, “the absence of a constitutional command is not an invitation to government complacency.” Singleterry, 29 F.3d at 741. Happily, the United States Sentencing Commission’s Special Report to Congress on Cocaine and Federal Sentencing Policy recommends that Congress revisit the 100 to 1 sentencing ratio.

For the foregoing reasons, we affirm.  