
    UNITED STATES of America, Plaintiff-Appellee, v. Gerard SMITH, AKA Gerard Robert Smith, Defendant-Appellant. United States of America, Plaintiff-Appellee, v. Maricela Long, Defendant-Appellant. United States of America, Plaintiff-Appellee, v. Gregory Thompson, Defendant-Appellant. United States of America, Plaintiff-Appellee, v. Mickey Manzo, AKA Mickey Shane Manzo, Defendant-Appellant. United States of America, Plaintiff-Appellee, v. Scott Craig, AKA Scott Alan Craig, Defendant-Appellant. United States of America, Plaintiff-Appellee, v. Stephen Leavins, Defendant-Appellant. United States of America, Plaintiff-Appellee, v. James Sexton, Defendant-Appellant.
    No. 14-50440, No. 14-50441, No. 14-50442, No. 14-50446, No. 14-50449, No. 14-50455, No. 14-50583
    United States Court of Appeals, Ninth Circuit.
    Argued and Submitted July 5, 2016 Pasadena, California
    Filed August 4, 2016
    
      Todd W. Burns (argued), Burns & Cohan, Attorneys at Law, San Diego, California, for Defendant-Appellant Stephen Leavins.
    William J. Genego (argued), Law Office of William Genego, Santa Monica, California, for Defendant-Appellant Gerard Smith.
    Karen Lee Landau (argued), Law Offices of Karen L. Landau, Oakland, California, for Defendanb-Appellant Scott Craig.
    Thomas P. O’Brien (argued), Paul Hastings LLP, Los Angeles, California, for Defendant-Appellant James Sexton.
    Hillary Potashner, Federal Public Defender; Gail Ivens and Elizabeth Richardson-Royer, Deputy Federal Public Defenders; Federal Public Defender’s Office, Los Angeles, California; for Defendant-Appellant Maricela Long.
    Kevin McDermott, Law Offices of Kevin Barry McDermott, Irvine, California, for Defendant-Appellant Gregory Thompson.
    Matthew J. Lombard, Matthew J. Lombard Law Offices, Los Angeles, California, for Defendant-Appellant Mickey Manzo.
    L. Ashley Aull (argued), Assistant United States Attorney; Lawrence S. Middleton, Chief, Criminal Division; Eileen M. Decker, United States Attorney; Office of the United States Attorney, Los Angeles, California; for Plaintiff-Appellee.
    Before: FERDINAND F. FERNANDEZ, RICHARD R. CLIFTON, and MICHELLE T. FRIEDLAND, Circuit Judges.
   OPINION

FERNANDEZ, Circuit Judge:

Gerard Smith, Maricela Long, Gregory Thompson, Mickey Manzo, Scott Craig, Stephen Leavins (collectively, the “Joint Appellants”), and James Sexton each appeal their convictions for obstruction of justice and conspiracy to obstruct justice. See 18 U.S.C. §§371, 1503(a). Long and Craig also appeal their convictions for making false statements. See id. § 1001(a)(2). Craig and Leavins also appeal their sentences. The Joint Appellants and Sexton raise a number of challenges to the jury instructions. We affirm.

BACKGROUND

The Joint Appellants and Sexton were all members of the Los Angeles Sheriffs Department (LASD), and were convicted for their roles in interfering with a federal investigation into civil rights abuses at Los Angeles County jails. Leavins, Craig, and Long were members of the Internal Criminal Investigations Bureau (ICIB), an LASD unit that investigates criminal activity by LASD employees. Leavins was a lieutenant, while Craig and Long were sergeants. Thompson was a lieutenant who oversaw Operation Safe Jails (OSJ), an LASD unit that investigates inmates. Smith, Manzo, and Sexton were OSJ deputies.

A federal grand jury began to investigate allegations of civil rights violations in LASD jails in June 2011. The grand jury issued subpoenas to LASD that month, seeking documents regarding “use of force” incidents in jails. The Federal Bureau of Investigation (FBI) assisted the grand jury with its investigation. By late-August 2011, a number of grand jury subpoenas had been served, and were circulated among LASD personnel, including some of the Joint Appellants.

As part of the federal investigation, in July 2011, the FBI used an undercover agent to bribe LASD Deputy Gilbert Michel to smuggle a cell phone to Anthony Brown, a cooperating inmate at LASD’s Men’s Central Jail (MCJ). The phone was intended to allow Brown to communicate contemporaneously with the FBI about claims of civil rights violations.

On August 8, 2011, LASD personnel found and seized the cell phone. Brown’s possession of the cell phone was treated much like similar conduct by other inmates, until August 18, 2011, when Smith, Manzo, and Thompson learned that Brown and his cell phone were linked to an FBI civil rights investigator. That prompted Thompson to impose stringent restrictions on Brown, including “no phones, no visits, especially from outside LE [law enforcement] without my approval.” It also prompted Smith and Manzo, later joined by Leavins, to interview Brown regarding the cell phone, civil rights violations, and the nature of Brown’s involvement with the FBI.

On August 23, 2011, FBI Agents Leah Marx, Wayne Plympton, and David Dahle went to MCJ to interview Brown and determine what happened to the cell phone. About an hour after the interview began, it was terminated by an LASD sergeant who entered the room shouting that the FBI agents did not have permission to interview Brown; Brown was taken away, and the FBI agents left after telling Brown they would return for him. Shortly thereafter, Smith, Manzo, Leavins, and LASD Captain William Carey interviewed Brown about the details of his meeting with the FBI, including whether Brown was going to testify. Leavins told Brown that he would be transferred to another jail for his safety, and promised Brown additional privileges there.

Brown was moved to a medical ward in MCJ while they decided where to transfer him, and by that night, he was under 24-hour guard by OSJ deputies. The guards were told that no one, including federal law enforcement, could visit or' see Brown. One guard testified that he knew that the FBI had given Brown a phone in connection with the investigation of illegal use of force in MCJ, and that the reason Brown had to be removed from MCJ was because the FBI was going to come to get him.

On August 24, 2011, Brown was interviewed again, this time by Manzo, Smith, Leavins, Craig, and Long. The interview immediately focused on the FBI, with Long asking Brown when he first came in contact with the FBI, what they were interested in, and who Brown’s FBI contacts were. Brown told them that the FBI was primarily focused on assaults in the jail.

Meanwhile, believing that their investigation may have been compromised, the FBI approached both Deputy Michel and his girlfriend, Deputy Angela Caruso, on August 24, 2011. They served Deputy Caruso with a grand jury subpoena.

On August 25, 2011, the federal district court issued a writ for Brown’s testimony before the federal grand jury; the writ required Brown’s production on September 7, 2011. The United States Marshals employee responsible for serving writs followed her usual practice of calling LASD prior to service; she was initially told that Brown could not be found, and then that the person would have to speak to a supervisor. The employee remembered faxing or emailing the writ to LASD thereafter, and telephone records confirmed two different faxes from the Marshals to LASD on the morning of August 25, 2011. LASD had no record of receiving the writ, but LASD personnel did become aware of it.

Later that afternoon, OSJ deputies went to LASD’s records office and asked that Brown be the released from the computer system. Although the clerks in the records office were reluctant to do so without a court order, they ultimately relented and “released” Brown. Sexton used his knowledge of LASD’s computer systems to assist in rebooking Brown under an alias; Brown was thereafter released and re-booked under a series of aliases, each time without information linking the alias to his true identity. That made it impossible for the FBI, the Marshals, and anyone in LASD’s Warrants and Detainers section to find Brown.

By the next day, August 26, 2011, Brown had been moved from MCJ to a jail in San Dimas, California. He continued to be guarded around the clock, and Deputy Sexton was one of those guards. Smith told one of Brown’s guards that the FBI should not be allowed to speak to Brown, and that he needed to be hidden from any federal agency. At 10:30 that night, Craig and Long interviewed Brown again, mocking whether the FBI would return for him and whether the FBI could “take the [LASD] house down,” as they had promised to do, since “the house [was] still there.”

Several days later, on August 30, 2011, Leavins, Craig, and Long interviewed Deputy Michel. Michel told them that the FBI had questioned him about the use of excessive force in the jail, subpoenaed his girlfriend (Deputy Caruso), and asked him to cooperate with their investigation into misconduct. Leavins, Craig, and Long sought to dissuade Michel from cooperating, telling him that the FBI was manipulating him, lying to him, threatening him, and blackmailing him. Craig ordered Michel not to discuss these matters with anyone, including the FBI.

That afternoon, Leavins, Craig, and Long interviewed Deputy William Cour-son, who had alerted his supervisors that he had contact with Agent Marx outside of work. Leavins, Craig, and Long attempted to discourage Courson from cooperating with the FBI by leading him to believe he “was played” and “lied to” by Agent Marx. Craig and Leavins told Courson not to talk to anyone about this, and Craig told him that if he was threatened with a “Federal Grand Jury Subpoena” or “[s]ome nonsense like that” he should call Craig.

That same day, LASD received three additional grand jury subpoenas dated August 24, 2011, which included requests for records regarding Brown and Deputies Michel and Caruso. On August 31, 2011, Manzo’s investigation notebook memorialized a meeting regarding “Fed. Grand Jury Inv. Subpoenas” and listed categories of documents requested with dates corresponding to the due dates of the August 24th subpoenas.

Brown was returned to MCJ by September 2, 2011, where he was interviewed briefly by Smith. Brown told Smith that he would have “nothing to do with [the FBI] anymore.” The next day, Brown wrote a letter addressed to several LASD personnel, including Long and Leavins, confirming that he would not testify for the FBI, and that the evidence he had given to them would therefore “mean[ ] nothing.” On September 12, 2011, Sexton re-booked Brown under his true name, and Brown was transferred to state custody that night.

Sometime during September 2011, an ICIB task force was created to investigate the use of force in jails and the cell phone found in Brown’s possession. Leavins was the lead lieutenant, Craig and Long were lead investigators, and Smith and Manzo were.members. In that first week after the creation of the task force, a shared drive that included all the federal grand jury subpoenas was established for the task force members.

On September 8, 2011, Craig applied for a state-court order requiring the FBI to produce materials regarding its investigation, but it was denied for lack of jurisdiction. The next day, Craig left a voicemail on a phone he believed to be Agent Marx’s, stating that he was working on a warrant for her arrest. On September 13, 2011, members of the LASD Special Operations Group began to surveil Agent Marx at Craig’s request. They tracked her to her apartment, identified her car, and followed her to work. Long and Craig then confronted Marx outside her apartment on September 26, 2011. Craig asked Marx if she knew she was “a named suspect in a felony complaint,” and told her that he was “in the process of swearing out a declaration for an arrest warrant for you.”

After this confrontation, Marx returned to the FBI office at the direction of her supervisor, Agent Narro. Narro called Craig and Long to ask them if there would be a warrant for Marx’s arrest, and Long told him “[t]here’s going to be,” and that it could be issued as soon as the next day. After the phone call, Long mocked Narro, saying “They’re scared! They’re like, do you know when[] is the warrant — ” and the room broke into laughter before the recording ended. As a result of these threats to Marx, the FBI agents postponed going to the jail to interview inmates and gather information because they were concerned that Marx would be arrested. No one on the investigation team returned to the jail for three months.

The Joint Appellants and Sexton were indicted for obstruction of justice and conspiracy to obstruct justice. In addition, Craig and Long were indicted for making false statements to the FBI. The Joint Appellants were tried, were convicted on all counts, and were sentenced to prison terms. Sexton was tried separately. His first trial ended in a mistrial, but his second trial resulted in his conviction on all counts. He was then sentenced to a prison term. These appeals followed.

JURISDICTION AND STANDARDS OF REVIEW

The district court had jurisdiction pursuant to 18 U.S.C. § 3231. We have jurisdiction pursuant to 18 U.S.C. § 3742(a) and 28 U.S.C. § 1291.

We review the district court’s “precise formulation” of jury instructions for abuse of discretion. United States v. Lloyd, 807 F.3d 1128, 1165 (9th Cir. 2015) (quoting United States v. Dixon, 201 F.3d 1223, 1230 (9th Cir. 2000)); see also United States v. Sarno, 73 F.3d 1470, 1485 (9th Cir. 1995). We review constitutional challenges, and whether the jury instructions misstated an element of the crime or adequately presented the defendant’s theory of his case, de novo.

We review for plain error those claimed errors that were not brought to the attention of the district court. Fed. R. Crim. P. 52(b); see also United States v. Pelisamen, 641 F.3d 399, 404 (9th Cir. 2011); United States v. Gomez-Norena, 908 F.2d 497, 500 (9th Cir. 1990).

DISCUSSION

There is little dispute about the conduct on which the Joint Appellants’ and Sexton’s indictments and convictions were predicated. Certain of them guarded Brown, transferred him to a new jail under various aliases, discouraged Brown and Deputies Michel and Courson from cooperating with the FBI, confronted FBI Agent Marx, and lied to her and her supervisor. Tape recordings, documents, and witness testimony (including from some of the appellants themselves) confirmed those activities. But whether the Joint Appellants and Sexton were guilty of the charged crimes crucially turned on the intent with which they acted. According to the Government, all acted with unlawful intent, and all were therefore guilty. According to the Joint Appellants and Sexton, all acted in good faith, motivated by an intent to follow orders, or to protect Brown from harm, or to investigate the FBI’s complicity in smuggling contraband, or to conduct their own investigation into civil rights abuses. The juries in each trial determined that the Government’s version was correct and convicted the Joint Appellants and Sexton.

Appellants now claim that a number of instructional errors undermined the verdicts. The Joint Appellants and Sexton all challenge jury instructions from their respective trials. In reviewing those challenges we will keep in mind the admonition that an instruction “may not be judged in artificial isolation, but must be viewed in the context of the overall charge,” and “the relevant inquiry is whether the instructions as a whole are misleading or inadequate to guide the jury’s deliberation.” Lloyd, 807 F.3d at 1164 (quoting Dixon, 201 F.3d at 1230).

(1) Intent required for obstruction of justice

The Joint Appellants argue that the jury instructions misstated the intent that the Government had to prove for obstruction of justice, which, they assert, allowed the jury to convict them merely for obstructing an FBI investigation, rather than for obstructing the grand jury. We do not agree.

In order to violate 18 U.S.C. § 1503(a), a defendant must have acted “with an intent to influence ... grand jury proceedings,” not to influence “an investigation independent of the ... grand jury’s authority.” United States v. Aguilar, 515 U.S. 593, 599, 115 S.Ct. 2357, 2362, 132 L.Ed.2d 520 (1995). This court has already held that “a grand jury investigation constitutes a judicial proceeding for purposes of § 1503.” United States v. Duran, 41 F.3d 540, 544 (9th Cir. 1994); see also United States v. Macari, 453 F.3d 926, 936 (7th Cir. 2006). Thus, the district court’s use of the phrase “grand jury investigation,” rather than “grand jury proceeding,” was neither misleading nor an abuse of discretion in these circumstances.

We also see no possibility that the jury understood “grand jury investigation” to refer to things the FBI may have done as part of an investigation independent of the grand jury’s authority. First, the jury instructions referred to a grand jury investigation, not an FBI investigation, and we presume that jurors follow their instructions. See United States v. Heredia, 483 F.3d 913, 923 (9th Cir. 2007) (en banc). Second, the evidence showed that the investigation was a grand jury investigation into civil rights abuses at LASD jails, and there was no evidence that the FBI’s efforts during this period were undertaken independently of the grand jury. See United States v. Hopper, 177 F.3d 824, 830 (9th Cir. 1999); see also United States v. Triumph Capital Grp., Inc., 544 F.3d 149, 169 (2d Cir. 2008); cf. Aguilar, 515 U.S. at 600-601, 115 S.Ct. at 2362-63.

There was no need for the district court to give an additional instruction proposed by the Joint Appellants which stated that it was insufficient for the Government to show that they obstructed an FBI investigation, as opposed to a grand jury investigation. To the extent that the FBI was operating as an arm of the grand jury, the trial jury was entitled to consider the Joint Appellants’ obstructive acts as they related to the FBI. See Macari, 453 F.3d at 936-38; see also Triumph Capital, 544 F.3d at 169; cf. Aguilar, 515 U.S. at 600-601, 115 S.Ct. at 2362-63. It was not told to do otherwise. Although the Joint Appellants now claim that the district court should have given yet another instruction explaining what the Government must show to demonstrate that the FBI was acting as an arm of the grand jury, they never proposed one. Review is therefore for plain error, but the Joint Appellants have not cited to any case that requires an instruction on that point and have not demonstrated that one was needed here. In fact, the other instructions told the jury that the Joint Appellants had to act with an intent to obstruct the grand jury investigation itself. Even if the failure to give an arm of the grand jury instruction sua sponte might be plain error in some circumstances, it would undoubtedly be harmless on this record. See United States v. Cherer, 513 F.3d 1150, 1155 (9th Cir. 2008). The evidence at trial pointed to the FBI’s acting for the grand jury, and the Joint Appellants do not identify any evidence on which the jury could rely to find that the FBI was acting “separate and apart” from the grand jury investigation. See Macari, 453 F.3d at 936-38.

There was also no plain error in the district court’s failure to give an instruction sua sponte that the Joint Appellants had to know that their conduct would have the “natural and probable effect” of influencing a grand jury investigation. See Aguilar, 515 U.S. at 599, 115 S.Ct. at 2362 (quoting United States v. Wood, 6 F.3d 692, 695 (10th Cir. 1993)); see also Duran, 41 F.3d at 544. They claim that is required by Aguilar, but we have previously described that decision as requiring that there be a nexus between the agency (here the FBI) activity and the judicial proceeding, and that the jury can infer that nexus “if the ‘natural and probable effect’ of the defendant’s conduct vis a vis the [FBI] proceeding would obstruct justice.” United States v. Bhagat, 436 F.3d 1140, 1147 (9th Cir. 2006) (quoting Aguilar, 515 U.S. at 599, 115 S.Ct. at 2362). The district court here gave a nexus instruction that was substantively identical to the one that was jointly proposed by the Joint Appellants and the Government, and that accurately reflected the law. See United States v. Fleming, 215 F.3d 930, 938 (9th Cir. 2000); see also United States v. Bonds, 784 F.3d 582, 587-88 (9th Cir. 2015) (en banc) (N.R. Smith, J., concurring). To the extent that Triumph Capital states that an additional instruction is required, we disagree. Aguilar does not require that essentially redundant instruction. Moreover, the instructions did require that the Government prove not only that the Joint Appellants’ actions would have had the natural and probable effect of interfering with the grand jury investigation, but also that the Joint Appellants did those acts “corruptly,” that is, with the purpose of obstructing justice.

The district court’s instructions regarding the intent required for obstruction of justice were correct and did not permit the jury to convict the Joint Appellants on the invalid theory that they obstructed an independent FBI investigation. We see no reason to believe that the jury’s general verdict was based on a failure to follow the specific instructions regarding grand jury investigations while concomitantly seizing upon and crediting the factually-unsupported theory that the Joint Appellants obstructed an independent FBI investigation. See Griffin v. United States, 502 U.S. 46, 59-60, 112 S.Ct. 466, 474, 116 L.Ed.2d 371 (1991) (refusing to negate a verdict on the chance “that the jury convicted on a ground that was not supported by adequate evidence when there existed alternative grounds for which the evidence was sufficient” (quoting United States v. Townsend, 924 F.2d 1385, 1414 (7th Cir. 1991))); see also United States v. Fulbright, 105 F.3d 443, 451 n.5 (9th Cir. 1997), overruled on other grounds by Heredia, 483 F.3d at 921-22; cf. McDonnell v. United States, 579 U.S. -, 136 S.Ct. 2355, 2374-75, 195 L.Ed.2d 639 (2016).

(2) Dual purposes

The Joint Appellants and Sexton challenge an instruction, given by the district court in each trial, which told the jury that the Government did not need to prove that the defendants’ sole or primary purpose was to obstruct justice. They all argue that the instruction should have required the Government to prove that their unlawful purpose was the sole or primary purpose. Sexton further explicates that position by arguing that the district court should have instructed the jury that the unlawful purpose had to be dominant.

We reject the claim that a defendant’s unlawful purpose to obstruct justice must be sole or primary. A defendant’s unlawful purpose to obstruct justice is not negated by the simultaneous presence of another motive for his overall conduct. We noted that over two decades ago. See United States v. Laurins, 857 F.2d 529, 537 (9th Cir. 1988). In that case, the Internal Revenue Service sent a summons to a company of which Laurins was a director. It sought production of books and records, but Laurins concealed them instead. Id. at 533-34. He was prosecuted for obstruction, and we held that the concealment fell within the definition of corruptly obstructing justice. Id. at 536-37. He claimed that his intent was to wait until he was personally summoned so that he could “assert his fifth amendment privilege.” Id. at 537. While that was a benign motive, we declared that it did not suffice to overcome the evidence of his corrupt motive to frustrate enforcement of the original summons. Id. at 537; see also United States v. Thomas, 916 F.2d 647, 651 (11th Cir. 1990) (“conduct [must be] prompted, at least in part, by a ‘corrupt motive’ ” (quoting United States v. Brand, 775 F.2d 1460, 1465 (11th Cir. 1985))); United States v. Howard, 569 F.2d 1331, 1336 n.9 (5th Cir. 1978) (same); United States v. Fayer, 523 F.2d 661, 663 (2d Cir. 1975) (the good motive was “outweighed” by the bad motive). And in a different context, we have recognized that where the purpose of an act was necessary to a conviction, it was not required to be the “primary or sole purpose” of that act. United States v. Banks, 514 F.3d 959, 969 (9th Cir. 2008).

The evidence was sufficient to suggest various motives for the Joint Appellants’ and Sexton’s conduct, so it was appropriate for the court to give an instruction regarding dual purposes. See Heredia, 483 F.3d at 923-24. Alternatively, the jury could have found that the Joint Appellants and Sexton undertook certain actions without a purpose to obstruct, but had that obstructive purpose with respect to other actions. See id. The instruction properly conveyed that concept. See Banks, 514 F.3d at 964-65, 969-70.

Sexton, however, adds that the district court’s clarification that “the purpose must be more than merely incidental” was not specific enough about where the strength of the purpose must fall on a continuum between “merely incidental” and sole or primary. At the district court he indicated that the jury should be told that the obstruction motive must be dominant and nothing less than that would do. The district court did not accept his position. Sexton relied on Banks in support of his argument. However, what Banks said was that in the “gang or racketeering enterprise” area the “purpose does not have to be the only purpose or the main purpose.” Id. at 969. “But it does have to be a substantial purpose.” Id. Banks then went on to say that it must be “one of the defendant’s general purposes or dominant purposes.” Id. at 970.

“Incidental” itself can be commonly defined as “subordinate, nonessential, or attendant in position or significance.... ” Webster’s Third New International Dictionary 1142 (Philip Babcock Gove, 3d ed. 1986). Thus, it would seem that, under the instruction given, the jury would have understood that the purpose must be essential in some sense — that is, substantial. Taken alone, “dominant” has a meaning of “commanding, controlling, or having supremacy or ascendancy over all others.” Id. at 671. Plainly, however, we did not mean in Banks that the purpose in question must be the dominant purpose, hence our use of the phrase “one of.” As we made clear in Banks, in the gang or racketeering area, when a person has two criminal purposes neither has to dominate (be the main purpose), but then neither can be “merely incidental” either. More simply put, perhaps, both purposes must be substantial. In any event, our effort in Banks does demonstrate the difficulty in attempting to wrap words around the common sense idea that in order to be liable for a crime premised on gang involvement a person’s criminal purpose must not only include the commission of a substantive crime, but also must include the additional criminal purpose of committing that .crime as a gang-oriented activity. See Banks, 514 F.3d at 969.

Nonetheless, we see the use of the phrase “merely incidental” in instructions as infelicitous. So, too, is use of the word “dominant.” Both should be eschewed. “Incidental” has a flavor that suggests that the standard is very low, even if that is not true as a definitional matter. “Dominant” has a flavor that suggests that the standard is very high. “Substantial” would convey the idea with more precision, but we decline to engagein the fascinating pursuit of choosing the exact word at this time— should it be “substantial” or “considerable” or “essential” or “significant” or “important” or “integral” or “strong,” etc.? We decline because, regardless of the exact word used, on this record the jury would not have been misled by the instruction that was given. The jury was not asked to decide an issue where one alleged purpose was very strong and the other very weak. It had to choose between two starkly different stories and readings of the evidence, but none of the argued purposes appeared to be asthenic in nature. In another case, the “more than merely incidental” formulation may well lead to error, and that makes its use rather dangerous at best; thus, our admonition against using it. But on this record, we find no reversible error in the instruction given.

We also reject Sexton’s claim that the degree of unlawful purpose required by 18 U.S.C. § 1503 is so ambiguous that the statute must be construed in his favor. He has identified no “grievous ambiguity” in the statute, and we see none. See Banks, 514 F.3d at 968. Moreover, we are confident that the mens rea required for a violation of the statute provides sufficient protection from conviction for law enforcement officers who are conducting lawful investigations without the requisite unlawful intent. See United States v. Lee, 183 F.3d 1029, 1032-33 (9th Cir. 1999).

(3) Good faith

Although in general “[a] defendant is not entitled to a separate good faith instruction,” the district court gave one. The Joint Appellants challenge the instruction on the ground that it suggested that good faith was merely some evidence inconsistent with unlawful intent, not a complete defense to the charged crime. Of course, as described above, the evidence adduced at trial suggested that the Joint Appellants may have had a variety of motives for their conduct — some of which were consistent with good faith, and some of which were consistent with a purpose to obstruct justice. Good faith as to one purpose did not mean good faith as to all of them, and the good faith instruction properly conveyed that concept. Because the instruction was correct, it is immaterial that its precise wording differed from the one used in a different trial. See United States v. Kilbride, 584 F.3d 1240, 1249 n.5 (9th Cir. 2009).

To the extent that the Joint Appellants claim that this instruction may have allowed the jury to convict them of obstruction even if it determined that they acted exclusively in good faith, we are not convinced. Read in the context of the other instructions, which specified that the Government had- to show that the defendants “acted corruptly ... with the intent to obstruct the federal grand jury investigation,” “with the purpose of obstructing justice,” and with “the unlawful intent to obstruct a grand jury investigation,” there is no real likelihood that the jury would have drawn that far-fetched inference. See Thomas, 612 F.3d at 1122; Kilbride, 584 F.3d at 1249-50; see also Middleton v. McNeil, 541 U.S. 433, 438, 124 S.Ct. 1830, 1833, 158 L.Ed.2d 701 (2004) (per curiam) (proposed “interpretation would require ... a rare combination of extremely refined lawyerly parsing of an instruction, and extremely gullible acceptance of a result that makes no conceivable sense”).

(4) Innocent Intent

Joint Appellants also assert that the district court erred because it failed to give an instruction proposed by some of them which was intended to indicate that the Joint Appellants’ intent was innocent — not unlawful — because they relied on ordei’s from superior officers whom they reasonably believed had authority to issue the orders. Essentially, that is an innocent intent defense. As we said in United States v. Burrows, 36 F.3d 875 (9th Cir. 1994):

[T]he defendant may allege that he lacked criminal intent because he honestly believed he was performing the otherwise-criminal acts in cooperation with the government. “Innocent intent” is not a defense per se, but a defense strategy aimed at negating the mens rea for the crime, an essential element of the prosecution’s case....

Id. at 881 (second alteration in original) (quoting United States v. Baptista-Rodriguez, 17 F.3d 1354, 1368 n.18 (11th Cir. 1994)); see also United States v. Jumah, 493 F.3d 868, 873-75 (7th Cir. 2007). That is, they do not seek to rely upon an excuse for the commission of a crime, rather they assert that they committed no crime at all. It is notable, however, that the Joint Appellants do not contend that they were committing criminal acts under orders or otherwise. Their- contention is not that they were ordered to do anything that would be criminal (for example, hiding a person for the purpose of obstructing a grand jury investigation), but rather that the acts were intrinsically innocent (for example, hiding a person to shield him from danger). In any event, what their proposed instruction amounted to was a claim that they acted in good faith, and the good faith instruction that was given did incorporate the superior-officer order concept already. The instructions adequately covered the Joint Appellants’ claim that they did not have the requisite intent to obstruct. See United States v. Sayakhom, 186 F.3d 928, 939-40 (9th Cir.), amended by 197 F.3d 959, 959 (9th Cir. 1999). The district court did not abuse its discretion in refusing to give the additional innocent intent instruction.

(5) California law

The Joint Appellants also argue that the district court wrongly instructed the jury regarding the legality of the FBI’s actions under California law. The instruction told the jury that certain sections of the California penal code “require the possession or introduction of contraband to be unauthorized in order for crimes to occur,” and that “[i]f Anthony Brown possessed any contraband including a cellular phone at the direction of the FBI, such possession or introduction of contraband would be authorized and no violation of these California Penal codes would have occurred.” See Cal. Penal Code §§ 4573(a), 4575(a).

The Joint Appellants and the Government dispute whether that instruction was correct as a matter of California law, and what impact the Supremacy Clause has in these circumstances. But we need not parse those issues for purposes of this opinion because even if we assume, without deciding, that the instruction was incorrect, it is not a basis for overturning the verdicts.

The Joint Appellants were not prejudiced by any error. See United States v. Frega, 179 F.3d 793, 806 n.16 (9th Cir. 1999); see also Cherer, 513 F.3d at 1155. They claim otherwise on the theory that if there was no crime, they could not investigate. However, that incorrect view was explicitly contradicted by the jury instructions. The jury was told that “[a] local officer has the authority to investigate potential violations of state law,” which “includes the authority to investigate potential violations of state law by federal agents.” The district court also told, counsel that they could argue that the Joint Appellants had the right to conduct their investigation. In light of the clear instruction regarding the Joint Appellants’ authority to investigate, any error in the instruction regarding whether or not federal agents actually violated California law was undoubtedly harmless. See Cherer, 513 F.3d at 1155.

(6) Instructions regarding the false statement counts

Craig and Long challenge the district court’s instructions regarding the false statement counts, primarily on the ground that the district court’s dual purposes instruction erroneously told the jury that it could convict them if they acted in good faith. But the dual purposes instruction did not apply to the false statement charges; it applied to the obstruction charges. It mentions obstruction of justice three times, and appears in a section of the instructions discussing obstruction of justice.

Similarly, the good faith instruction did not apply to the false statement count, nor was the court asked to give one for that count. In any event, because the jury was properly instructed on the elements of the false statement offense, the district court was not required to instruct on good faith. In short, the false-statement instructions required the jury to find that Craig and Long acted willfully with a purpose to disobey the law. Those instructions left no room for the jury to convict Craig and Long if they acted entirely in good faith. See Green, 745 F.2d at 1210.

CONCLUSION

There is little dispute about what Appellants did, but a good deal of conflict about why they did it — their intent, their motives, their purposes. They say that all was done for benign purposes but the Government says that what they did was for criminal purposes. Ultimately, a properly instructed jury had to decide whose narrative it believed — the amaranthine essence of the jury function. These juries were properly instructed, and accepted the Government’s position.

AFFIRMED. 
      
      . They have also raised several other challenges to their convictions and sentences. We have addressed those in a memorandum disposition filed on the same date as this opinion.
     
      
      . In setting forth the background, we have “considered] the evidence presented at trial in the light most favorable to the prosecution.” United States v. Nevils, 598 F.3d 1158, 1164 (9th Cir. 2010) (en banc).
     
      
      . In grand jury testimony that was admitted at his trial, Sexton said that he learned from LASD personnel in the Warrants and Detain-ers section that a writ for Brown had been received, and that he told Smith and Manzo.
     
      
      . There was testimony that around this time, LASD personnel were told that, if a federal agent came to a facility to serve a writ for Brown, LASD Undersheriff Paul Tanaka’s cell phone should be called and the writ not honored. The message was disseminated in person so that there would be no written record of it and no chance for it to be captured on telephones that could be “bugged.”
     
      
      . United States v. Purdy, 264 F.3d 809, 811 (9th Cir. 2001); United States v. Larson, 495 F.3d 1094, 1101 (9th Cir. 2007) (en banc).
     
      
      . Lloyd, 807 F.3d at 1164-65; see also Sarno, 73 F.3d at 1485.
     
      
      . As relevant to this argument, the instructions given to the jury read as follows:
      In order for each defendant to be found guilty of [obstruction of justice], the Government must prove each of the following elements beyond a reasonable doubt.
      First, the defendant influenced obstructed or impeded or tried to influence, obstruct, or impede a federal grand jury investigation;
      And second, the defendant acted corruptly with knowledge of a pending federal grand jury investigation and with the intent to obstruct the federal grand jury investigation. '
      As used in Section 1503 "corruptly” means that the act must be done, with the purpose of obstructing justice. The government does not need to prove that defendants’ conduct had the actual effect of obstruction. However, the Government must prove that the defendants’ actions would have had the natural and probable effect of interfering with the grand jury investigation.
      One element the Government must prove beyond a reasonable doubt with respect to the obstruction of justice charges is that the defendant had the unlawful intent to obstruct a grand jury investigation.
     
      
      . See Henderson v. United States, - U.S. -, 133 S.Ct. 1121, 1124, 1126-27, 1130-31, 185 L.Ed.2d 85 (2013); see also United States v. Houser, 130 F.3d 867, 872 (9th Cir. 1997) (review is for plain error when no alternative instruction was proposed and no objection was made to the failure of the district court to give an alternative instruction).
     
      
      . See supra note 7 (fourth paragraph of quoted material).
     
      
      . In Bonds, the "natural and probable effect” element of § 1503 was characterized as a "materiality requirement.” Framed either as a nexus element or a materiality element, there is no requirement that the defendant, in addition to the specific intent to obstruct justice, also have knowledge that his acts may have the "natural and probable effect” of interfering with justice.
     
      
      . Triumph Capital, 544 F.3d at 166-67 & n.16.
     
      
      . Aguilar, 515 U.S. at 599, 115 S.Ct. at 2362.
     
      
      . Id. at 601, 115 S.Ct. at 2363.
     
      
      . United States v. Rasheed, 663 F.2d 843, 852 (9th Cir. 1981). The Joint Appellants also challenge Rasheed's definition of “corruptly” as overly broad, but we are bound by that precedent and apply it here. See Miller v. Gammie, 335 F.3d 889, 899 (9th Cir. 2003) (en banc).
     
      
      . We also reject the Joint Appellants’ argument that tampering with grand jury witnesses is not a legally permissible theory under 18 U.S.C. § 1503. See United States v. Hernandez, 730 F.2d 895, 898 (2d Cir. 1984). This court has already held to the contrary. See United States v. Ladum, 141 F.3d 1328, 1337-38 (9th Cir. 1998). We are bound by that precedent. See Miller, 335 F.3d at 899.
     
      
      .In the Joint Appellants' trial, the instruction said:
      The Government need not prove that the defendants’ sole or even primary purpose was to obstruct justice so long as the Government proves beyond a reasonable doubt that one of the defendants’ purposes was to obstruct justice. The defendants’ purpose of obstructing justice must be more than merely incidental.
      The instruction was the same in Sexton’s trial, mutatis mutandis.
     
      
      . United States v. Green, 745 F.2d 1205, 1209 (9th Cir. 1984); see also United States v. Shipsey, 363 F.3d 962, 967 (9th Cir. 2004).
     
      
      . The instruction provided:
      Evidence that a defendant relied in good faith on the orders the defendant received from the defendants’ superior officers and that the defendant reasonably and objectively believed those orders to be lawful is inconsistent with an unlawful intent and is evidence you may consider in determining if the Government has proven beyond a reasonable doubt that a defendant had the required unlawful intent.
      If you find, however, that a defendant carried out those orders with an unlawful intent to obstruct a grand jury investigation or that a defendant did not reasonably and objectively believe the superiors’ orders to be lawful, the defendants' conduct is not excused by a claim or evidence that the defendant might have been following orders of his or her superiors.
     
      
      . See Lloyd, 807 F.3d at 1164.
     
      
      . We also reject the Joint Appellants’ claim that the prejudice they suffered from this instruction was exacerbated by the district court’s finalizing the instruction after closing arguments. Indeed, they have not demonstrated that their closing arguments were undermined by the change. Moreover, they were given- an opportunity to object both before and after the court delivered the instructions but did not do so. Cf. United States v. Liu, 731 F.3d 982, 987-88 (9th Cir. 2013). Finally, they did not express surprise or seek further argument time. Cf. United States v. Hannah, 97 F.3d 1267, 1269 (9th Cir. 1996).
     
      
      . The proposed instruction read:
      The defendants contend that to the extent he committed the acts alleged to constitute the charged crimes, his acts were authorized by a law enforcement official who he reasonably believed had such authority.
      In order for the defendant to be guilty of the charged offenses, the government must prove beyond a reasonable doubt that the defendant’s acts were not authorized by a law enforcement officer or that it was not reasonable for the defendant to believe the law enforcement had such authority.
     
      
      
        . See United States v. Doe, 705 F.3d 1134, 1145-46 (9th Cir. 2013); Jumah, 493 F.3d at 874-75.
     
      
      . See supra note 18.
     
      
      . U.S. Const. art. VI, cl. 2.
     
      
      . We do not consider Craig and Long’s claim that an innocent intent instruction should have been given with respect to the false statement counts because they did not propose one and raised the issue only in their reply brief. See United States v. Romm, 455 F.3d 990, 997 (9th Cir. 2006).
     
      
      
        .See supra note 16.
     
      
      . The district court instructed:
      [T]he Government must prove each of the following elements beyond a reasonable doubt:
      First the defendant made a false statement in a matter within the jurisdiction of the Federal Bureau of Investigation.
      Second, the defendant knew the statement was false.
      Third, the defendant acted willfully.
      And fourth, the statement was material to the activities or decisions of the Federal Bureau of Investigation. That is, it had a natural tendency to influence or was capable of influencing the agency’s decisions or activities.
      The word "willfully” means that the defendant made the statement voluntarily and purposely and with knowledge that the defendants’ making of the statement was unlawful. That is, the defendant must have made the statement with a purpose to disobey or disregard the law.
      This is in accord with the statutory language of the offense. See 18 U.S.C. § 1001; see also United States v. Camper, 384 F.3d 1073, 1075 (9th Cir. 2004) ("The government must prove five elements to obtain a conviction for making a false statement under § 1001; (1) a statement, (2) falsity, (3) materiality, (4) specific intent, (5) agency jurisdiction.”). Craig and Long do not argue that the instruction was incorrect.
     
      
      . See Shipsey, 363 F.3d at 967; Green, 745 F.2d at 1209.
     