
    UNITED STATES of America, Appellee, v. Randall MARTINEZ, a/k/a Randall, a/k/a Jose Rodriguez, a/k/a Jose Rodriguez-Saez, a/k/a Rando Martinez, a/k/a Randall Martinez-Espinal, Henry Fiorentino, Jose Tejada, and Marcos Rodriguez, a/k/a Markito, Defendants-Appellants.
      
    
    Docket Nos. 14-2759, 15-511, 15-836, 15-1001, 15-3699
    August Term, 2016
    United States Court of Appeals, Second Circuit.
    Argued: October 19, 2016
    Decided: July 7, 2017
    
      ALEXANDER SOLOMON, SYLVIA SHWEDER, Assistant United States Attorneys, Brooklyn, New York (Robert L. Capers, United States Attorney for the Eastern District of New York, Emily Berger, Assistant United States Attorney, Brooklyn, New York, on the brief), for Appellee.
    MARYBETH COVERT, Assistant Federal Public Defender, Buffalo, New York (Marianne Mariano, Federal Public Defender, Jayme L. Feldman, Assistant Federal Public Defender, Buffalo, New York, on the brief), for Defendant-Appellant Martinez.
    JAMES M. BRANDEN, New York, New York, for Defendant-Appellant Fior-entino; Defendant-Appellant Fiorentino also filed briefs pro se.
    ROBERT CALIENDO, New York, New York (Maurice H. Sercarz, Sercarz & Rio-pelle, New York, New York, on the brief), for Defendant-Appellant Tejada.
    EPHRAIM SAVITT, New York, New York, for Defendant-Appellant Rodriguez.
    Before: KEARSE, JACOBS, and POOLER, Circuit Judges.
    
      
       The Clerk of Court is respectfully directed to amend the caption as set forth above.
    
   KEARSE, Circuit Judge:

Defendants Randall Martinez (“Martinez”) and Marcos Rodriguez (“Rodriguez”) appeal from judgments entered in the United States District Court for the Eastern District of New York by Sandra L. Townes, Judge, and defendants Henry Fiorentino and Jose Tejada appeal from judgments entered in that court by John Gleeson, Judge, convicting all four defendants of conspiracy to commit Hobbs Act robbery, in violation of 18 U.S.C. § 1951(a), and conspiracy to distribute narcotics, in violation of 21 U.S.C. § 846; convicting Martinez and Rodriguez of brandishing a firearm in furtherance of a crime of violence and/or narcotics trafficking, in violation of 18 U.S.C. § 924(c)(1)(A)(ii); and convicting Tejada of obstruction of an official proceeding, in violation of 18 U.S.C. § 1512(c)(2), and conspiring to obstruct an official proceeding, in violation of id. § 1512(k). Defendants were sentenced principally to prison terms of 264 months for Martinez, 264 months for Fiorentino, 216 months for Te-jada, and 272 months for Rodriguez. On appeal, Martinez, who entered pleas of guilty in two related cases in two district courts, challenges the adequacy of his plea hearing and the denial of his requests for new counsel in the Eastern District case. The other defendants, convicted following their respective jury trials, principally raise statute-of-limitations arguments and/or evidentiary challenges to their trial proceedings and challenge their sentences. For the reasons that follow, we .find no basis for overturning any of the challenged convictions or sentences.

I. OVERVIEW

The present prosecutions arise out of a sprawling conspiracy in and around New York City, spanning at least a decade, in which more than two dozen persons are alleged to have committed more than 200 robberies of drug traffickers. One of the coconspirators’ main stratagems was to impersonate officers of the New York City Police Department (“NYPD”) in order to stop or purport to arrest drug traffickers and search their vehicles or to enter and search premises where the coconspirators had been informed that drugs might be located.

The record includes evidence that. Fior-entino was a leader of crews in the conspiracy, that Rodriguez was one of his principal lieutenants, and that they participated in numerous robberies and thereafter sold their shares of the stolen narcotics. Martinez participated in many robberies, generally as a getaway driver or a lookout. Tejada, for much of the period covered by the conspiracy, was in fact an NYPD police officer. He participated in robberies, and he provided co-conspirators with genuine police equipment and with information about ongoing criminal investigations' in which they might be targeted.

Many indictments and superseding indictments were handed down, and one or more of the present defendants appeared before various judges in two federal judicial districts. While the conduct of these defendants was part of the same overall conspiracy, some were active in different branches of it and at different times than others, and none of these defendants were tried together. We consider each defendant’s challenge to his convictions in turn.

II. FIORENTINO

Fiorentino was charged in a November 18, 2009 three-count indictment with conspiracy to commit robbery affecting interstate commerce, in violation of 18 U.S.C. § 1951(a) (“Hobbs Act robbery”) (Count One), conspiracy to distribute narcotics, in violation of 21 U.S.C. § 846 (Count Two), and using a firearm in furtherance of a crime of violence and narcotics trafficking, in violation of 18 U.S.C. §§ 924(c)(l)(A)(ii) and 2 (Count Three). In 2014, having earlier pleaded guilty before Judge Townes but been allowed to withdraw that plea, he was tried before Judge Gleeson and a jury. After the government rested its case, the court dismissed Count Three on the ground that there was insufficient evidence of Fiorentino’s use of a gun during the statute-of-limitations period; Fiorentino was found guilty on the other two counts and was sentenced principally to 264 months’ imprisonment, to be followed by a five-year term of supervised release.

On appeal, Fiorentino contends principally that the evidence at his trial was insufficient to prove that he was a member of the conspiracy within the statute-of-limitations period and that his sentence was substantively unreasonable. In pro se supplemental briefing, he argues principally that use of evidence with regard to the seizure of some of his property violated his rights under the Fourth and Sixth Amendments. We find no merit in any of his contentions.

A. The Evidence

The evidence at Fiorentino’s trial included testimony from six of his coconspira-tors, each of whom had committed robberies with Fiorentino — and with Rodriguez as Fiorentino’s “right-hand man” — from approximately 1997 through 2003. They testified in detail about numerous such events in which Fiorentino, leading a shifting cast of supporting characters, dressed as a plainclothes police officer and drove vehicles that were outfitted to look and operate like unmarked police cruisers in order to facilitate robberies of drug dealers. For example, on a tip to coconspirator Sandy Beato in or about 2003 about an impending sale of cocaine, Fiorentino, with Rodriguez, Beato, and one of the other testifying coconspirators, watched the robbery target leave a house in the Bronx and drive off in a truck. The crew followed and soon forced the truck to stop. Beato testified that Fiorentino, dressed in civilian clothes but with a bulletproof vest, a holstered gun, handcuffs, and a badge, spoke with the driver for several minutes. The crew found five kilograms of cocaine in the truck; Rodriguez and Beato drove away with it. Fiorentino pretended to recruit the driver of the truck to be an informant, promising to return the cocaine if he would tell Fiorentino about future drug sales; The five kilograms of cocaine were divided equally among the four robbers and the tipster.

On another 2003 tip — this time that 160 kilograms of cocaine were present in a certain apartment in a Bronx housing complex — Fiorentino and coconspirator Gabriel Cano-Martinez, outfitted with police clothing, equipment, and badges, went to that apartment, identified themselves as policemen,. and handcuffed the occupants. Cano-Martinez testified that they found $120,000 in cash and 126 kilograms of cocaine, of which he and Fiorentino kept a total of $40,000 and 38 kilograms of cocaine, giving the rest of the cash and drugs to the tipsters. Rodriguez helped Fiorenti-no sell his share of the cocaine.

Fiorentino at. trial conceded that he had participated in the conspiracy for a time, but he argued that he had withdrawn from the conspiracy prior to the start of the five-year statute-of-limitations period, see 18 U.S.C. § 3282(a), ie., prior to November 18, 2004; and each of the cooperating witnesses against him testified that they committed no robberies with him after 2003. However, those witnesses also testified that ■ they themselves continued to commit such robberies and that neither they nor Fiorentino expressed any intention to stop committing robberies together. In addition, some testified that they discussed with Fiorentino committing future robberies after November 2004. Cano-Martinez, who encountered Fiorentino in the Dominican Republic on several occasions in 2006, testified that they “talked about the possibility of getting back together here in the United States.... [t]o rob again together.” And Beato, who encountered Fiorentino in jail in or after 2009, testified that Fiorentino asked why Beato had not contacted him “to work” after their 2003 robberies. When Beato said he had not known how to reach Fior-entino, Fiorentino said Beato could have contacted him through Rodriguez.

In addition, encounters between Fioren-tino and bona fide NYPD officers revealed that he was well equipped to continue robbery operations after 2004. In a January 2005 stop, officers found in Fiorentino’s vehicle handcuffs, a handcuff key, and a replica police badge. In June 2006, officers stopped Rodriguez in a vehicle registered to Fiorentino; upon searching the car, they found a police placard and a police scanner. A later inventory search also uncovered three police badges and naturalization papers, apparently forged, in Fiorentino’s name. In September 2006, the police searched Fiorentino’s residence, with his consent, and found, inter alia, a police-style flashlight, guns and fake guns, bullets and blanks, wrist restraints, and police radios. There was also sales-records evidence of purchases of this type of equipment by Fiorentino in 2005 and 2006.

In October 2006, an NYPD detective investigating Fiorentino and Rodriguez seized a Chevrolet Impala that was equipped with lights, sirens, and a PA system of the type found in unmarked police cruisers. An inventory search found handcuffs, holsters, two NYPD rain jackets, and two police shields. The car was registered to Rodriguez and had been seized from a parking spot leased to Fior-entino.

Rodriguez was arrested in November 2006 and told the arresting officers that Fiorentino had some property stored in Rodriguez’s sister’s apartment. In a subsequent search with the sister’s consent, the officers found, inter alia, branding stamps for heroin packages, a scale, an NYPD K-9 baseball cap, an orange EZ-Pass of the type used by police officers, fake firearms, holsters, handcuffs, bulletproof vests, a police scanner, NYPD jackets, NYPD-style cargo pants, and replica police patches.

B. The Statute-of-Limitations Defense

Fiorentino does not challenge the sufficiency of the government’s evidence to prove that there existed a conspiracy of which he was a member and that the conspiracy itself continued in existence well into the limitations period. However, he contends that he had withdrawn from the conspiracy more than five years before he was indicted on November 18, 2009, and that the district court should therefore have granted his posttrial motions pursuant to Fed. R. Crim. P. 29 and 33 for acquittal or a new trial. Rule 29 provides that “the court on the defendant’s motion must enter a judgment of acquittal of any offense for which the evidence is insufficient to sustain a conviction.” Fed. R. Crim. P. 29(a); see generally United States v. Eppolito, 543 F.3d 25, 45 (2d Cir. 2008) (“Eppolito”) (“The test for sufficiency ... is whether a rational jury could conclude beyond a reasonable doubt that a defendant is guilty of the crime charged.” (internal quotation marks omitted)), cert. denied, 555 U.S. 1148, 129 S.Ct. 1027, 173 L.Ed.2d 313 (2009). Rule 33 provides that “the court may vacate any judgment and grant a new trial if the interest of justice so requires.” Fed. R. Crim. P. 33(a). We see no error or abuse of discretion in the court’s denial of those motions.

“Conspiracy is generally a continuing crime,” meaning that its commission “ ⅛ not complete until the purposes of the conspiracy have been accomplished or abandoned.’” Eppolito, 543 F.3d at 47 (quoting United States v. Rastelli, 870 F.2d 822, 838 (2d Cir.), cert. denied, 493 U.S. 982, 110 S.Ct. 515, 107 L.Ed.2d 516 (1989)). Accordingly, the limitations period begins only when the purposes of the conspiracy have been accomplished or abandoned. Once the government “has presented sufficient evidence to show a conspiracy that has continuing purposes or goals” and that has continued into the limitations period, “the burden is on the defendant to prove ... that he took affirmative steps to withdraw.” Eppolito, 543 F.3d at 49; see also United States v. Spero, 331 F.3d 57, 60-61 (2d Cir.), cert. denied, 540 U.S. 819, 124 S.Ct. 100, 157 L.Ed.2d 36 (2003). “Unless a conspirator produces affirmative evidence of withdrawal, his participation in a conspiracy is presumed to continue until the last overt act by any of the conspirators.” United States v. Diaz, 176 F.3d 52, 98 (2d Cir.) (internal quotation marks omitted), cert. denied, 528 U.S. 875, 120 S.Ct. 314, 145 L.Ed.2d 153 (1999).

For a defendant to show that he withdrew from the conspiracy, proof merely that he ceased conspiratorial activity is not enough.... He must also show that he performed “some act that affirmatively established that he disavowed his criminal association with the conspiracy,” ... either the making of a clean breast to the authorities, or communication of the abandonment in a manner reasonably calculated to reach co-conspirators ....

Eppolito, 543 F.3d at 49 (quoting United States v. Eisen, 974 F.2d 246, 268 (2d Cir. 1992) (other internal quotation marks omitted), cert. denied, 507 U.S. 1029, 113 S.Ct. 1840, 123 L.Ed.2d 467 (1993)). To effect a withdrawal, the defendant’s disassociation with the conspiracy must be complete and permanent; he “ ‘must not take any subsequent acts to promote the conspiracy.’ ” Eppolito, 543 F.3d at 49 (quoting United States v. Berger, 224 F.3d 107, 118 (2d Cir. 2000)).

And ‘“[wjhile arrest or incarceration may constitute a withdrawal from a conspiracy, it does not follow that in every instance it must’ rather, it is merely a relevant fact that entitles the defendant to a jury instruction on withdrawal. United States v. Flaharty, 295 F.3d 182, 192 (2d Cir.) (quoting United States v. Agueci, 310 F.2d 817, 839 (2d Cir. 1962), cert. denied, 372 U.S. 959, 83 S.Ct. 1016, 10 L.Ed.2d 12 (1963) (emphases in Agueci)), cert. denied, 537 U.S. 936, 123 S.Ct. 37, 154 L.Ed.2d 237 (2002).

The jury at Fiorentino’s trial was instructed, properly and without objection, with respect to his statute-of-limitations defense based on his claim of withdrawal from the conspiracy prior to November 18, 2004. The evidence described in Part II.A. above as to Fiorentino’s discussions with a coconspirator in 2006 as to his desire to participate in- additional robberies, and as to his conversations with another cocon-spirator in or after 2009 questioning why he had not been asked to do so, was more than sufficient to permit a rational inference that Fiorentino had not withdrawn from the conspiracy. And his continued readiness to participate in the conspiracy’s robberies of drug dealers and distribution of narcotics was amply confirmed by records of Fiorentino’s police-equipment purchases in 2005 and 2006, and by police discoveries in January of 2005 and in June, September, October, and November of 2006 of his drug distribution paraphernalia such as a scale and a money counter and/or his NYPD garments and badges enabling intimidation and restraint of drug dealers while posing as a police officer. In sum, there was abundant evidence on which to permit the jury to find that Fior-entino’s membership in the conspiracy continued into the limitations period.

Fiorentino also challenges his sentence. {See Part YI.C. below.)

C. Other Challenges

In a pro se supplemental brief, Fiorentino argues principally that the district court’s admission of certain evidence against him violated his rights under the Fourth and Sixth Amendments. His Fourth Amendment argument, liberally construed, is that evidence from the 2006 seizure and search of the Impala and the search of Rodriguez’s sister’s apartment should have been suppressed because the searches were conducted without warrants. This argument is not properly preserved.

A request for “suppression of evidence,” “must be raised by pretrial motion if the basis for the motion is then reasonably available and the motion can be determined without a trial on the merits.” Fed. R. Crim. P. 12(b)(3)(C). A “suppression argument that was made in an untimely fashion before the district court” is waived “unless there is a showing of cause.” United States v. Yousef, 327 F.3d 56, 125 (2d Cir.) (argument waived where the defendant “had ample opportunity to raise and develop [his] argument before the District Court and he has not provided ... any reasonable excuse for his failure to so”), cert. denied, 540 U.S. 933, 124 S.Ct. 353, 157 L.Ed.2d 241 (2003). Here there is no indication in the record that Fiorentino ever moved in the district court to suppress the evidence in question. Further, when he was specifically asked at trial whether he had any objection to the admission of proffered evidence that had been found in the Impala or in Rodriguez’s sister’s apartment, he answered, “None” (Fiorentino Trial Transcript at 610, 621). Accordingly, his present objection has been waived.

Nor is there any substantive basis for Fiorentino’s argument that the government’s failure to call Detective Armando Rodriguez as a witness at trial violated his Sixth Amendment right of confrontation as announced in Crawford v. Washington, 541 U.S. 36, 59, 124 S.Ct. 1354, 158 L.Ed.2d 177 (2004) (“[t]estimonial statements of witnesses absent from trial [may be] admitted only where the declarant is unavailable, and only where the defendant has had a prior opportunity to cross-examine”). At Fiorentino’s trial, another detective testified that Detective Rodriguez was involved in these investigations and in the arrest of defendant Marcos Rodriguez; but the government did not offer in evidence any statements by Detective Rodriguez.

Finally, to the extent that Fiorentino’s supplemental pro se reply brief contains arguments not made in either his opening pro se brief or the brief filed by his attorney, we decline to consider them. “[N]ew arguments may not be made in a reply brief.” Ernst Haas Studio, Inc. v. Palm Press, Inc., 164 F.3d 110, 112 (2d Cir. 1999).

III. RODRIGUEZ

Rodriguez, like Fiorentino, was indicted on November 18, 2009, and on the same counts: Hobbs Act robbery conspiracy, 18 U.S.C. § 1951(a) (Count One), narcotics distribution conspiracy, 21 U.S.C. § 846 (Count Two), and using a firearm in furtherance of the robbery and drug distribution conspiracies, 18 U.S.C. § 924(c)(l)(A)(ii) (Count Three). Unlike Fiorentino, Rodriguez did not assert a § 3282(a) statute-of-limitations defense at or prior to trial; and at Rodriguez’s trial before Judge Townes, all three counts were submitted to the jury. In July 2011, the jury found Rodriguez guilty on all counts; in addition, the jury made express findings that the gun referred to in Count Three had been used in connection with the robbery conspiracy and that it had been brandished.

In June 2014, some three years after the verdicts were returned, but before he was sentenced, Rodriguez moved pursuant to Fed. R. Crim. P. 29 and 33 for acquittal on all three counts, arguing for the first time that there was no evidence of his participation in the charged conspiracy after November 18, 2004, i.e., during the five-year statute-of-limitations period. He argued that if he was involved in any conspiracy after the limitations period, it was a separate conspiracy from that charged in the indictment. The district court denied the motions, stating that the jury could reasonably infer that there was a single conspiracy until at least 2008 and that Rodriguez never withdrew from it.

In January 2015, two months after Fior-entino succeeded in having the gun count against him dismissed, Rodriguez supplemented his Rule 33 motion, arguing that the interest of justice reqúired a ruling in Rodriguez’s favor on Count Three to parallel the ruling in Fiorentino’s case. The district court again denied the motion, stating that Judge Gleeson’s dismissal of the firearm count against Fiorentino may have been based on evidence different from that presented at the trial of Rodriguez, and that the evidence at Rodriguez’s trial was not based on firearm seizures beyond the statute-of-limitations period.

The court eventually sentenced Rodriguez principally to 188 months’ imprisonment on the conspiracy counts and to the mandatory consecutive, statutory minimum, seven-year term on Count Three for brandishing the firearm — for a total of 272' months’ imprisonment — to be followed by five years of supervised release.

On appeal, Rodriguez’s sole contention is that the court should have granted his motion under Rule 29 or Rule 33 on the ground that there was insufficient evidence at his trial to prove that anyone involved in the predicate conspiracies committed any firearms offenses in furtherance of the conspiracies after the summer of 2004, and thus his conviction on Count Three, with its severe mandatory penalties, was barred by the statute of limitations. As Rodriguez did not timely assert his statute-of-limitations defense in the district court, we conclude that it has been waived. See generally Musacchio v. United States, — U.S. -, 136 S.Ct. 709, 716-18, 193 L.Ed.2d 639 (2016).

“Commission of [a federal] crime within the statute-of-limitations period is not an element of the ... offense.” Smith v. United States, 568 U.S. 106, 112, 133 S.Ct. 714, 184 L.Ed.2d 570 (2013) (emphasis in original). Rather, “ ‘it is up to the defendant to raise the limitations defense’ the § 3282(a) statute of limitations “becomes part of a case only if the defendant presses it in the district court” “at or before trial.” Musacchio, 136 S.Ct. at 717-18 (quoting Smith, 568 U.S. at 112, 133 S.Ct. 714).

When a defendant presses a limitations defense, the Government then bears the burden of establishing compliance with the statute of limitations by presenting evidence that the crime was committed within the limitations period or by establishing an exception to the limitations period.... When a defendant fails to press a limitations defense, the defense does not become part of the case and the Government does not otherwise have the burden of proving that it filed a timely indictment.

Musacchio, 136 S.Ct. at 718 (first emphasis in original; second emphasis added).

A statute-of-limitations defense not raised “at or before trial” is not reviewable on appeal. Id. Not even plain-error review can come to the rescue because, if the defendant did not raise the statute-of-limitations defense at or prior to trial, “there is no error for an appellate court to correct — and certainly no plain error.” Id. (emphasis added).

As Rodriguez did not raise his present statute-of-limitations contention until long after his trial, the district court, properly denied his motion for acquittal. And we see no abuse of discretion in the court’s conclusion that a new trial was not warranted in the interest of justice.

IV. TEJADA

Tejada — an NYPD officer — was charged in 2013 in a six-count superseding indictment (“Sll”): the Hobbs Act robbery conspiracy, 18 U.S.C. § 1951(a) (Count One); the narcotics distribution conspiracy, 21 U.S.C. § 846 (Count Two); using a firearm in furtherance of the robbery and drug distribution conspiracies, 18 U.S.C. § 924(c)(l)(A)(ii) (Count Three); two counts of obstruction of justice, one by corruptly endeavoring to influence or impede the due administration of justice in connection with a federal grand jury proceeding in the Eastern District of New York, in violation of 18 U.S.C. § 1503(a) (Count Four), and the other by corruptly obstructing, influencing, and impeding a grand jury proceeding, or attempting to do so, in violation of 18 U.S.C. § 1512(c)(2) (Count Five); and one count of conspiring to violate § 1512(c)(2), in violation of id. § 1512(k) (Count Six).

Tejada went through two jury trials. He was first tried in 2013 before Judge Townes on the above six counts. The jury found him guilty on Counts Five and Six— the § 1512 substantive and conspiracy obstruction-of-justice counts — but was unable to reach agreement on the other four counts. In 2014, a four-count superseding indictment was filed (“S12”), recharging Tejada with the counts of the Sll indictment on which, at his 2013 trial, the jury had been unable to agree. The case was reassigned to Judge Gleeson, who presided over the second trial. After the close of the government’s evidence, Judge Gleeson dismissed Count Four, the § 1503(a) obstruction count. As to the remaining counts, the jury found Tejada guilty on Counts One and Two, Hobbs Act robbery conspiracy and narcotics distribution conspiracy, respectively, and not guilty on Count Three, use of a firearm.

The convictions on Counts Five and Six of Sll and Counts One and Two of S12 were consolidated for sentencing before Judge Gleeson, who sentenced Tejada principally to 216 months’ imprisonment, to be followed by a three-year term of supervised release.

On appeal, Tejada argues (1) that the evidence at his first trial was insufficient to support his convictions for obstruction of justice; (2) that the admission of certain out-of-court statements at his second trial was not permitted by Federal Rule of Evidence 801(d)(1)(C); and (3) that the prosecutor, in his rebuttal summation at the second trial, impermissibly vouched for the credibility of government witnesses and inflamed the jury. He also contends that his sentence is procedurally and substantively unreasonable (see Part VI.B below). We find no basis for reversal.

A. The Obstruction Convictions

The evidence with respect to the § 1512 obstruction counts on which Tejada was convicted at his first trial included internal police records as to searches by Tejada of NYPD databases, and testimony by several cooperating witnesses as to, inter alia, Tejada’s involvement in the conspiracies to rob drug dealers and to profit by selling the proceeds, including testimony from Yvan Tineo, a close friend of Tejada since the early 1990s and a member of the conspiracy since 2003, recruited by Cano-Martinez. In 2006, Tineo recruited Tejada, who was then a police officer, to join the conspiracy. Tineo testified about several robberies that he and Tejada committed either alone or with other coconspirators (see also Part IV.B. below), including NYPD officer Jorge Arbaje-Diaz, and about his own and Tejada’s reactions when law enforcement started closing in.

In March 2008, a sting operation resulted in the arrests of eight members of the conspiracy, including Cano-Martinez. Documentary evidence showed that two days later, Tejada searched NYPD databases for Tineo’s name. In October 2008, Arbaje-Diaz was arrested. He had committed robberies with, among others, Tejada, Tineo, and Tineo’s cousins Ivan and Ronald Pauli-no. Concerned that the investigation would soon lead to Tineo and the Paulinos, Tineo asked Tejada to search for their names through the NYPD computer system to check for arrest warrants. Tejada did so in January 2009 and reported to Tineo that the results were negative. Ivan Paulino, who had gone to the Dominican Republic in September 2008, testified that if the searches had revealed any arrest warrants in his name he would have remained in the Dominican Republic rather than come back to the United States.

There was .evidence that Tejada continued to conduct such searches throughout early 2009, and he ran several searches for his own name in January 2010. Tejada, testifying in his own defense, admitted, inter alia, that he had searched through law enforcement databases for the names of Tineo and the Paulinos and had communicated the results of his searches to Tineo. (See Tejada First Trial Transcript, November 13, 2013 (“Tejada 2013 Tr.”), at 2580-82).

Section § 1512 provides in pertinent part that
(c) Whoever corruptly—
(2) ... obstructs, influences, or impedes any official proceeding, or attempts to do so,
shall be fined under this title or imprisoned not more than 20 years, or both.
(k) Whoever conspires to commit any offense under this section shall be subject to the same penalties as those prescribed for the offense the commission of which was the object of the conspiracy-

18 U.S.C. §§ 1512(c)(2), (k) (emphasis added). “For the purposes of this section ... an official proceeding need not be pending or about to be instituted at the time of the offense.Id. § 1512(f)(1). However, the government must prove that such a proceeding was reasonably foreseeable to the defendant, see, e.g., Arthur Andersen LLP v. United States, 544 U.S. 696, 707-08, 125 S.Ct. 2129, 161 L.Ed.2d 1008 (2005); United States v. Binday, 804 F.3d 558, 590-91 (2d Cir. 2015) (“Binday”), cert. denied, — U.S. -, 136 S.Ct. 2487, 195 L.Ed.2d 823 (2016).

In addition, to prove obstruction of justice in violation of § 1512(c)(2), the government must show that there was a “nexus” between the defendant’s conduct and the pending, or foreseeable, official proceeding, see, e.g., United States v. Reich, 479 F.3d 179, 185-86 (2d Cir.) (“Reich”), cert. denied, 552 U.S. 819, 128 S.Ct. 115, 169 L.Ed.2d 26 (2007); id. (holding the “ ‘nexus requirement’ ” applied to 18 U.S.C. § 1503 by United States v. Aguilar, 515 U.S. 593, 599-600, 115 S.Ct. 2357, 132 L.Ed.2d 520 (1995), equally applicable to a charge of obstruction in violation of § 1512(c)(2)). Elements of corruption and attempt of course require proof of some knowledge on the part of the defendant of an ongoing or foreseeable official proceeding. See generally Nye & Nissen v. United States, 336 U.S. 613, 620, 69 S.Ct. 766, 93 L.Ed. 919 (1949) (aiding and abetting theory supports liability when the defendant “consciously shares in” the underlying criminal act); United States v. Kumar, 617 F.3d 612, 621 (2d Cir. 2010) (“Kumar”) (to establish that an act was done corruptly, government must prove wrongful intent), cert. denied, 563 U.S. 1028, 131 S.Ct. 2931, 180 L.Ed.2d 238 (2011); Direct Sales Co. v. United States, 319 U.S. 703, 711-12, 63 S.Ct. 1265, 87 L.Ed. 1674 (1943) (“knowledge is the foundation of intent”). However, the existence of a nexus between his action and the proceeding does not depend on the defendant’s knowledge. See generally Binday, 804 F.3d at 590; Reich, 479 F.3d at 185; cf. Kumar, 617 F.3d at 621 (“a defendant does not need to know with certainty that his conduct would affect judicial proceedings”). Rather, the existence of a nexus, for obstruction-of-justiee purposes, is determined by whether the defendant’s acts “have a relationship in time, causation, or logic with the judicial proceedings.” Reich, 479 F.3d at 185 (quoting Aguilar, 515 U.S. at 599, 115 S.Ct. 2357).

The actions of the defendant need not have directly impeded, or attempted to impede directly, the official proceeding. The nexus requirement is satisfied where “‘discretionary actions of a third person [would be] required to obstruct the judicial proceeding’ if it was ‘foreseeable to [the defendant] that the third party ... would act on the [communication] in such a way as to obstruct the judicial proceeding.’” United States v. Desposito, 704 F.3d 221, 231-32 (2d Cir. 2013) (quoting Reich, 479 F.3d at 185).

Nor, to permit conviction under either § 1512(c)(2) or § 1503, need the defendant’s acts be successful in impeding or obstructing justice; “an ‘endeavor’ suffices” under § 1503, Aguilar, 515 U.S. at 599, 115 S.Ct. 2357 (quoting United States v. Russell, 255 U.S. 138, 143, 41 S.Ct. 260, 65 L.Ed. 553 (1921)), as does an “attempt” under § 1512(c)(2), e.g., Reich, 479 F.3d at 186-87, so long as his acts had the natural and probable consequence of interfering with an official proceeding that was foreseeable even if not then pending.

In the present case, it was easily infera-ble that the 2008 arrests of many of his coconspirators made it foreseeable to Teja-da — who estimated that as an NYPD officer, he had testified 15-20 times in grand jury proceedings (see Tejada 2013 Tr. 2457) — that there would be a grand jury proceeding leading to numerous indictments. And it could easily be inferred that Tejada’s persistent searches of NYPD databases, and his reports back to coconspir-ators who had not been arrested, were intended to make it possible for them to avoid arrest by absconding before any outstanding warrants could be executed, thereby potentially interfering with an ongoing grand jury proceeding. Indeed, Ivan Paulino — who was eventually arrested in 2010 when he attempted to reenter to the United States — testified that if Tejada’s searches had found Paulino’s name among those to be arrested, he would have remained in the Dominican Republic rather than returning to the United States.

We conclude that the evidence as a whole was sufficient to permit a rational juror to infer beyond a reasonable doubt that Tejada attempted to obstruct or impede the ongoing or foreseeable grand jury proceeding in the Eastern District of New York.

Tejada argues that Judge Gleeson’s dismissal, at the second trial, of the § 1503 count against him signified that there was no nexus between his acts and the grand jury proceeding. We disagree — as did Judge Gleeson when he ultimately considered that argument (see Tejada Sentencing Transcript (“T.S.Tr.”) 10-11 (“I credit th[e] testimony ... [of] those individuals whose names were searched in the police department database” who “were in the Dominican Republic at the time,” that they “would have been notified to ... stay away, which would essentially frustrate the purpose of the grand jury proceeding.”)).

B. Out-of-Court Descriptions of Attempted Robbers

Tejada contends that he is entitled to a new trial on the ground that hearsay evidence as to his participation in an attempted robbery was improperly admitted at his second trial. The attempt occurred in January 2007 at a house on Schley Avenue in the Bronx (the “Schley house”), where, according to a tip received by Tineo, 50 kilograms of cocaine were supposedly stored in the basement.

The residents of the Schley house, Rosa and Joseph Giordano, described the ordeal. They testified that three men, two of them wearing police attire and carrying guns, arrived at their home that night and sought entry, announcing that they were responding to a report of shots fired. While the man in plain clothes waited at the door, the police-attired men searched the house. After searching, one of them drew his gun and said he was going to handcuff the Giordanos for everyone’s safety; Mr. Giordano refused and became angry, suggesting that the men consult the Giordanos’ next-door neighbor who was a former policeman. The men then abruptly left the Schley house, after appearing to be in communication with a supervisor. They sped off in a brown car that looked like an unmarked police car, but with lights and sirens.

The Giordanos promptly called 911 about the incident. They gave the responding officers descriptions of the three men. More than three years later, in April 2010, NYPD investigators showed the Giordanos photo arrays in an attempt to have them identify the men who had been at their home. Rosa saw some faces that “looked like” those men but she could not identify anyone with certainty; Joseph could not identify anyone. At trial, Joseph testified that in January 2007 he and Rosa had described the men as best they could to the responding officers; but neither of the Giordanos testified to the descriptions they had given.

The government called as a witness one of the detectives who had responded to the Giordanos’ 911 call, and that officer was allowed to testify to the physical descriptions the Giordanos had given that night in January 2007. The court concluded that his testimony was admissible under a rule that provides that the court may admit a statement as nonhearsay if “[t]he declarant testifies and is subject to cross-examination about [the] prior statement, and the statement ... identifies a person as someone the declarant perceived earlier,” Fed. R. Evid. 801(d)(1)(C). Tejada contends that the detective’s testimony was instead impermissible hearsay, arguing that the rule applies only if the declarant of the out-of-court statement is the witness testifying to it in court.

We conclude that we need not resolve this issue because if admission of the detective’s testimony as to the Giordanos’ descriptions of the police imposters who came to the Schley house was error, it was beyond a reasonable doubt harmless. See, e.g., United States v. McGinn, 787 F.3d 116, 127 (2d Cir. 2015) (“even if a ruling was manifestly erroneous, we will still affirm if the error was harmless” — that is, “if it is not likely that it contributed to the verdict” (internal quotation marks omitted)).

Tineo himself testified in detail about the attempted robbery as follows. Shown a photograph of the Schley house, which both Giordanos had identified as the house in which they lived in January 2007, Tineo testified that he and Tejada had attempted to rob that home in January 2007, based on a tip that 50 kilograms of cocaine were stored in the basement. On that night Te-jada, having procured a burgundy unmarked police cruiser while on duty, drove Tineo and one of the tipsters to the Schley house.

Tineo testified that he and Tejada were wearing NYPD clothing. Tejada was armed with his service weapon, and Tineo was carrying a fake gun. They rang or knocked at the door, and Tejada announced that they were responding to a report of a disturbance. They were admitted by the Giordanos, who denied that there had been any disturbance at their home. Tejada and Tineo entered the house, while the tipster (who had accompanied Tejada and Tineo to ensure that the tipsters did not get cheated of their share of the loot) remained at the door. Tejada announced that, for everyone’s safety, he wanted to put Mr. Giordano in handcuffs. Mr. Giordano became irate and refused to be cuffed, saying that their neighbor was a police officer and would vouch for them. Tineo searched the basement and found no drugs.

Tineo became persuaded that their tip had brought them to the wrong house, in part because he found no evidence of any drugs and in part because in their experience as police impersonators robbing drug dealers, the drug dealers never resisted being handcuffed. Tineo signaled Tejada that they had the wrong house; Tejada agreed, and they headed for the door. Te-jada took out his radio and pretended to receive another call that they needed to respond to, and the three men departed in a hurry. The unmarked police car sped off with lights and sirens going.

In short, the testimony of Tineo describing the robbery attempt at the Schley house closely matched the descriptions of that event by the Giordanos, and his testimony made clear that the two robbers dressed as police officers were Tineo and Tejada.

Further, the Schley house attempted robbery was but a sliver of the evidence as to Tejada’s membership in the robbery conspiracy, for there was abundant detailed evidence that Tejada had participated in other robberies of drug dealers, as well as in other aspects of the conspiracy. For example, Tineo testified that he and Tejada robbed a drug courier in the Bronx and that he and Tejada, with the help of Tejada’s fellow NYPD officer Arbaje-Diaz, carjacked another drug courier in Manhattan. Tineo and two other coconspirators testified that Tejada participated in the staged arrest at JFK Airport of an airline employee who was a participant in a drug-smuggling operation seeking a bigger share of the drugs for himself. In addition, several coconspirators testified that Tejada provided police equipment for their robberies and that he allowed them to store police-impersonation equipment and stolen narcotics in his apartment. And virtually the same evidence was introduced at this trial as at Tejada’s first trial (see Part IV.A. above) describing his NYPD database searches in order to alert fellow co-conspirators as to whether they had been targeted for arrest.

In sum, the evidence that Tejada was a member of the robbery conspiracy was overwhelming. If it was error to admit the detective’s testimony as to the Giordanos’ descriptions of the attempted robbers, it was harmless beyond any reasonable doubt.

C. Challenges to the Government’s Summation

Tejada also contends that he should have a new trial on the ground that the government’s rebuttal summation at his second trial was improper and prejudicial. The government in its initial summation at that trial, anticipating that Tejada would challenge the credibility of the cooperating witnesses, argued to the jury that it should credit their testimony for three reasons: that their testimonies were consistent with each other and with other evidence, that they had no opportunity to coordinate their testimonies, and that they faced serious penalties if they were caught lying. In his defense summation, Tejada’s attorney argued that the jury should not trust the cooperating witnesses (a) because their repeated interviews with prosecutors and law enforcement agents had included discussion of false versions of the facts that they either had consciously adopted in order to increase their chances of leniency, or had unconsciously actually come to believe because of repeated suggestions, and (b) because the witnesses had been housed in the same detention facility and could have found ways to collude in crafting their testimony.

In the government’s rebuttal summation, the Assistant United States Attorney (“AUSA”) characterized the defense summation as arguing that the jury was presented with “nothing less than a jailbreak, with all the cooperating witnesses coming here to lie to you,” and argued that the defense scenario was “impossible.” He pointed out that several of the cooperating witnesses had failed to recognize other cooperating witnesses when shown their photographs, and argued that it was “impossible” for witnesses to collude with others they did not know, and that even if they were housed in the same detention facility “[t]he odds [we]re one in a billion or even worse” that “complete strangers could get together to collude to frame” someone.

Tejada’s counsel objected to the government’s dubbing his argument a “jailbreak” scenario. The district court overruled the objections, stating that the AUSA’s statements were “just argument” and “characterization[s]” that the jury could accept or reject. Tejada’s subsequent Rule 33 motion for a new trial on the ground that the government’s summation was inflammatory and that it vouched for the credibility of the cooperating witnesses, was also denied. On appeal, Tejada pursues his contention that he is entitled to a new trial on this basis. We disagree.

It is well established that prosecutors may not properly “use arguments calculated to inflame the passions or prejudices of the jury.” United States v. Modica, 663 F.2d 1173, 1180 (2d Cir. 1981) (internal quotation marks omitted), cert. denied, 456 U.S. 989, 102 S.Ct. 2269, 73 L.Ed.2d 1284 (1982). It is also well established that it is inappropriate for prosecutors to “vouch” for their witnesses’ truthfulness by “expressing their] personal belief or opinion as to the truth” of the testimony. Id. at 1178-79 (internal quotation marks omitted); see, e.g., id. at 1178 (“I’m here to tell you that Mr. Amato’s testimony when it relates to the evidence in this case is truthful,” constituted improper vouching).

However, while the government may not “vouch” for the credibility of its witnesses, it “is allowed to respond to an argument that impugns its integrity or the integrity of its case,” United States v. Carr, 424 F.3d 213, 227 (2d Cir. 2005) (“Carr”) (internal quotation marks omitted), cert. denied, 546 U.S. 1221, 126 S.Ct. 1447, 164 L.Ed.2d 145 (2006), and “[a] defendant who ... seeks to overturn his conviction based on alleged prosecutorial misconduct in summation bears a heavy burden,” United States v. Williams, 690 F.3d 70, 74-75 (2d Cir. 2012) (internal quotation marks omitted). We will reverse on this ground only if there was misconduct that “ ‘cause[d] the defendant substantial prejudice by so infecting the trial with unfairness as to make the resulting conviction a denial of due process.’ ” Carr, 424 F.3d at 227 (quoting United States v. Shareef, 190 F.3d 71, 78 (2d Cir. 1999)).

Tejada has not met this standard. The AUSA’s pointing to objective bases in the record for the jury to credit the testimony of the cooperating witnesses was not a personal attestation and did not constitute vouching for them. The AUSA’s colorful “jailbreak” and “one in a billion” language was clearly hyperbolic and would not have been taken by the jury literally. We see no denial of due process here.

V. MARTINEZ

Martinez was charged with crimes related to this robbery and drug distribution conspiracy in two districts: in the Eastern District of New York in April 2009 and in the Southern District of New York in April 2011. In November 2011 in the Eastern District, he pleaded guilty before Judge Townes to three offenses paralleling those of which Rodriguez was convicted, ie., Hobbs Act robbery conspiracy, 18 U.S.C. § 1951(a), narcotics trafficking conspiracy, 21 U.S.C. § 846, and use of a firearm in furtherance of those conspiracies, in violation of 18 U.S.C. §§ 924(c)(1)(A)(ii) and 2. In December 2011, with the understanding that his Southern District case would be consolidated with the Eastern District case for sentencing in the Eastern District, Martinez pleaded guilty in the Southern District before Judge Paul D. Gardephe to an attempt to commit a § 1951 Hobbs Act robbery that caused the death of the intended robbery victim.

Martinez’s Southern District case was then consolidated with his Eastern District case for sentencing before Judge Townes, who eventually sentenced Martinez principally to 264 months’ imprisonment, to be followed by a five-year term of supervised release. Notwithstanding that consolidation, Martinez has appealed separately with respect to his Eastern District convictions, in No. 14-2759, and his Southern District conviction, in No. 15-1001, and those appeals have been consolidated in this Court. In his brief on appeal, Martinez challenges only proceedings in the Eastern District case, contending that his requests for new counsel were denied in violation of his rights under the Sixth Amendment, and that in his plea allocution he was inadequately informed of the nature of the § 924(c) firearm charge. We reject both contentions.

When Martinez was charged in the Eastern District in 2009, the district court, pursuant to the Criminal Justice Act, appointed Marion A. Seltzer as his attorney. In the spring of 2010, Martinez wrote to Judge Townes asking that he be assigned new counsel, stating that Seltzer was “not helping [him] adequately in any of [his] needs regarding [his] case.” He wrote to the court again a few months later, complaining that Seltzer was not sensitive to Martinez’s lack of knowledge of English, that she did not come to visit him or keep him apprised of steps she was taking in his case, and that she did not inform him whether she had filed motions he requested. Prior to Martinez’s second letter, Seltzer had unsuccessfully moved for a bill of particulars, had discussed with Martinez the possibility of a guilty plea, and had participated in plea negotiations in his behalf. The court did not respond to Martinez’s change-of-counsel requests; Seltzer remained his attorney; and Martinez made no further requests for new counsel until 2013. In March 2011, Seltzer secured a six-to-seven-month postponement of Martinez’s Eastern District trial, in part to enable him to learn the outcome of his expected indictment in the Southern District before deciding whether to plead guilty in the Eastern District case.

A. The Eastern District Plea Allocution

In November 2011, at a conference scheduled for the discussion of pretrial matters, Martinez suddenly decided to plead guilty, without a plea agreement, to the first three counts of the pending superseding indictment. Both the court and Seltzer were caught by surprise; neither had brought a copy of the indictment, and while the court took a brief recess to gather the necessary materials, Seltzer and Martinez filled out the required paperwork in the courtroom.

The following exchanges then took place in open court between Judge Townes and Martinez, through an interpreter:

THE COURT: Have you been able to communicate without difficulty with your attorney?
THE DEFENDANT: Yes.
THE COURT: All right.
Now, have you had an opportunity to discuss your case fully with Ms. Seltzer?
THE DEFENDANT: Yes.
THE COURT: Are you satisfied to have her represent you?
THE DEFENDANT: Yes..

(Plea Hearing Transcript (“Martinez Tr.”) at 8, 10 (emphases added).) The court informed Martinez of the elements of each of his alleged' offenses. It then explained that he was charged in the Count Three gun charge on a theory of aiding and abetting:

THE COURT: .... [W]hat that means is that the government doesn’t have to prove that you actually carried a gun or firearm.
.... [Y]ou may be found guilty of Count Three if the jury finds beyond a reasonable doubt that the government has proven that another person actually committed the offense in Count Three, but you aided and abetted that person ... in the offense.
Do you understand that?
THE DEFENDANT: Yes.

(Martinez Tr. 16.) The court went on to explain some of the factors that are used to determine whether a person aided or abetted a crime; Martinez again stated that he understood. With respect to the gun charge, the following additional colloquy occurred:

THE COURT: And Count Three, use of a firearm, how do you plead?
THE DEFENDANT: Guilty.
THE COURT: All right. Tell me what you did with regard to this.
THE DEFENDANT: I helped other people to commit crimes. I never had any firearms, they had their firearms.
THE COURT: Were you aware they had firearms’!
THE DEFENDANT: Yes.
THE COURT: And did you intentionally aid these people to commit the crimes—
THE DEFENDANT: Yes.
THE COURT: —where they had firearms? What did you do?
THE DEFENDANT: I used to take them to the places, that was it.
THE COURT: Well, I thought you said you were a lookout.
THE DEFENDANT: Yes.
THE COURT: Okay. And there were others who actually went inside of the establishment?
THE DEFENDANT: Yes.
THE COURT: And they were armed? •
THE DEFENDANT: Yes. Sometimes yes, sometimes no.
THE COURT: All right. And when they were — you were aware of it as you were acting as a lookout?
THE DEFENDANT: Yes.
THE COURT: And did that happen when you committed Counts One and Two?
THE DEFENDANT: In some occasions they carried firearms and others no.
THE COURT: But during those occasions when they did carry firearms, you were present there as a lookouts
THE DEFENDANT: Yes.
THE COURT: And you knew that they were carrying firearms1!
THE DEFENDANT: Yes.
THE COURT: All right.

(Martinez Tr. 36-37 (emphases added).) After Martinez confirmed dates and locations of these 2005-2006 offenses, the court revisited the exact nature of his conduct:

THE COURT: And do you know of any occasions where they actually showed the firearms?
THE DEFENDANT: No. Mainly they used to be in their own vehicles.
THE COURT: All right. But you knew they had the gun, so it’s reasonably foreseeable.
THE DEFENDANT: Yes.
[AUSA]: And, your Honor, we do— the government has proof that he was on robberies where firearms were brandished and he was present during the brandishing of the firearms.
THE DEFENDANT: Not that I remember. I was not present when they did it.
I never had firearms in my own hands, but the others did. And it was possible that they would withdraw— draw their firearms.
THE COURT: If they had firearms, didn’t you expect them to use the firearms and display them?
THE DEFENDANT: Sometimes when they went on the robberies they showed a police badge. They didn’t necessarily have to pull out firearms. On some occasions they would pull their firearms out to scare people.

(Martinez Tr. 38-39 (emphasis added).)

No objection was made to any aspect of the plea proceeding. The court accepted Martinez’s plea of guilty to Counts One, Two, and Three of the pending superseding indictment. His plea of guilty in the Southern District case, to one count of Hobbs Act attempted robbery, was entered a month later.

B. Martinez’s Renewed Request for New Counsel

Martinez was not sentenced until July 2014. In the spring of 2013, he wrote to the court seeking to have what he perceived as errors in his presentence report (“PSR”) corrected prior to his sentencing date, despite being advised by counsel that disputes about the PSR would be resolved at the sentencing hearing. In July 2013, Seltzer filed a sentencing memorandum for Martinez that did not dispute the facts or the Sentencing Guidelines (“Guidelines”) calculations in Martinez’s PSR but discussed 18 U.S.C. § 3553(a) sentencing factors at some length in urging the court to depart downward from the advisory-Guidelines-recommended range of 360 months’ to life imprisonment and to sentence Martinez to the minimum required prison term of 204 months. In December 2013 and March 2014, Martinez wrote to the court requesting appointment of new counsel. His December 2013 letter tersely mentioned “the taking of [his] plea” and accused Seltzer, conclusorily, of “deliberate incompetence”; his 2014 letter stated con-clusorily that he and Seltzer were “NOT GETTING ALONG.”

Following the receipt of Martinez’s 2014 letter, the district court held a hearing on his motion to replace Seltzer. The court stated that it had reviewed Martinez’s letters and asked whether he wished to add anything. He said he did not. The court denied his motion, stating that it found no reason to appoint a new attorney.

We see no abuse of discretion, see, e.g., United States v. Jones, 482 F.3d 60, 75 (2d Cir. 2006), cert. denied, 549 U.S. 1231, 127 S.Ct. 1306, 167 L.Ed.2d 119 (2007), in this decision. Despite Martinez’s early requests for the replacement of Seltzer because of lack of adequate communication, he did not pursue those requests in the 14 months before he decided to plead guilty. In Martinez’s plea colloquy, the court asked whether Martinez had “been able to communicate without difficulty with [his] attorney” and whether he was “satisfied to have her represent [him]”; under oath, he answered “Yes” to both questions. The district court was not required to doubt the sincerity of those sworn answers.

In the post-guilty-plea pre-sentencing period, Martinez made only conelusory complaints about Seltzer; and he declined to elaborate when the court asked if he wished to do so at the hearing convened to explore his complaints. His motion for new counsel was properly denied.

C. The Sufficiency of the Count Three Plea Allocution

Martinez’s contention that he was not sufficiently informed about the firearm count to make his plea of guilty to that count knowing and voluntary fares no better. Rule 11 imposes the strict requirement that the court, before accepting a plea of guilty, must “address the defendant personally in open court” and, inter alia, “inform the defendant of, and determine that the defendant understands ... the nature of each charge to which the defendant is pleading.” Fed. R. Crim. P. 11(b)(1)(G). “ “What is essential ... is that the court determine by some means that the defendant actually understands the nature of the charges.’” United States v. Torrellas, 455 F.3d 96, 102 (2d Cir. 2006) (“Torrellas”) (quoting United States v. Maher, 108 F.3d 1513, 1521 (2d Cir. 1997)). “ ‘[I]n all such inquiries, matters of reality, and not mere ritual, should be controlling.’ ” Torrellas, 455 F.3d at 102 (quoting McCarthy v. United States, 394 U.S. 459, 467 n.20, 89 S.Ct. 1166, 22 L.Ed.2d 418 (1969)).

Further, where, as here, the defendant has failed to make a timely Rule 11 objection in the district court, we conduct only plain-error review, see United States v. Dominguez Benitez, 542 U.S. 74, 76, 80, 124 S.Ct. 2333, 159 L.Ed.2d 157 (2004); United States v. Vonn, 535 U.S. 55, 58-59, 122 S.Ct. 1043, 152 L.Ed.2d 90 (2002). Under the plain-error standard, we decline to reverse unless the defendant “ ‘demonstrate^ that (1) there was error, (2) the error was plain, (3) the error preju-dicially affected his substantial rights, and (4) the error seriously affected the fairness, integrity or public reputation of judicial proceedings.’ ” United States v. Adams, 768 F.3d 219, 223 (2d Cir. 2014) (quoting United States v. Cook, 722 F.3d 477, 481 (2d Cir. 2013)), cert. denied, — U.S. -, 135 S.Ct. 1726, 191 L.Ed.2d 694 (2015). “In order to establish that a Rule 11 violation affected ‘substantial rights,’ the defendant must show ‘that there is “a reasonable probability that, but for the error, he would not have entered the plea.” ’ ” United States v. Pattee, 820 F.3d 496, 505 (2d Cir.) (quoting United States v. Vaval, 404 F.3d 144, 151 (2d Cir. 2005) (which was quoting Dominguez Benitez, 542 U.S. at 83, 124 S.Ct. 2333)), cert. denied, — U.S. -, 137 S.Ct. 222, 196 L.Ed.2d 171 (2016).

Although Martinez contends that he “was openly confused and defensive about the facts surrounding the § 924(c) Count and did not understand the ways in which he could be held liable for this charge” (Martinez brief on appeal at 45), the record does not support this contention. In the plea hearing colloquy quoted in detail in Part V.A. above, the court explained that since Martinez was charged in Count Three with “aiding and abetting” the use of firearms, “the government d[id]n’t have to prove that [Martinez] actually carried a gun or a firearm,” and that he could be “found guilty of Count Three if the jury [were to] find[ ] beyond a reasonable doubt that the government has proven that another person actually committed the offense in Count Three, but [Martinez] aided and abetted that person ... in the offense.” (Martinez Tr. 16.) Martinez said he understood.

Although Martinez also suggests that the court’s mention, at one point, of foreseeability (see id. at 38) indicated that it accepted his plea on a theory of Pinkerton liability, see Pinkerton v. United States, 328 U.S. 640, 646-48, 66 S.Ct. 1180, 90 L.Ed. 1489 (1946) (defendant may be held hable for a substantive offense committed by a coconspirator if that offense was a reasonably foreseeable consequence of the conspiratorial agreement), rather than on an aiding-and-abetting theory, we see no indication that that is so. The court repeatedly asked Martinez about his actual knowledge of the use of guns and about what he did to provide assistance. Martinez unequivocally answered, “I helped other people to commit crimes.... [T]hey had their firearms.” (Martinez Tr. 36.) He stated that he “knew that they were carrying firearms”; that he “intentionally aidfed] these people to commit the crimes”; that he “used to take them to the places” where they “actually went inside of the establishment”; that “[s]ometimes when they went on the robberies they showed a police badge. They didn’t necessarily have to pull out firearms. On some occasions they would pull their firearms out to scare people”; and that “during those occasions when they did carry firearms, [he] w[as] present there as a lookout.” (Id. at 36-37, 39 (emphases added).)

Finally, Martinez’s suggestion that if he had understood the Pinkerton theory of liability, “he likely would have taken his chance at trial on this charge” (Martinez brief on appeal at 47) borders on the frivolous. Learning that there were two bases for conviction (aiding/abetting and Pinkerton), not just one, would logically have made the desirability of taking a chance on trial not greater but less.

In sum, we see no error in the court’s acceptance of Martinez’s plea of guilty to aiding and abetting others in brandishing firearms in furtherance of the Hobbs Act robbery conspiracy; and, if there was error, we see no possibility that Martinez could meet the plain-error standard.

VI. SENTENCING CHALLENGES BY TEJADA AND FIORENTINO

Fiorentino contends that his sentence was substantively unreasonable. Tejada contends that his sentence was both procedurally and substantively unreasonable.

A. General Sentencing Principles

Procedural errors in sentencing include “failing to calculate” the advisory Guidelines range, “improperly calculating” that range, “failing to consider the § 3553(a) factors,” or “selecting a sentence based on clearly erroneous” factual findings. Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007); see, e.g., United States v. Cavera, 550 F.3d 180, 190 (2d Cir. 2008) (en banc) (“Cavera”), cert. denied, 556 U.S. 1268, 129 S.Ct. 2735, 174 L.Ed.2d 247 (2009); United States v. Johnson, 567 F.3d 40, 51 (2d Cir. 2009). The district court’s factual findings at sentencing need be supported only by a preponderance of the evidence. See, e.g., United States v. Salazar, 489 F.3d 555, 557 (2d Cir. 2007); United States v. Gaskin, 364 F.3d 438, 464 (2d Cir. 2004), cert. denied, 544 U.S. 990, 125 S.Ct. 1878, 161 L.Ed.2d 751 (2005).

“In reviewing a sentence, we will not overturn the district court’s findings of fact unless they are clearly erroneous.” United States v. Norman, 776 F.3d 67, 76 (2d Cir.) (“Norman”), cert. denied, — U.S. -, 135 S.Ct. 2333, 191 L.Ed.2d 995 (2015); United States v. Garcia, 413 F.3d 201, 221-22 (2d Cir. 2005). Credibility assessments by the judge who presided over the trial and sentencing proceedings, having an opportunity to hear and view the defendant and the witnesses, are entitled to considerable deference. See, e.g., Gall, 552 U.S. at 51-52, 128 S.Ct. 586; Norman, 776 F.3d at 76-77. “[W]here there are two permissible views of the evidence, the fact-finder’s choice between them cannot be clearly erroneous.” United States v. Abiodun, 536 F.3d 162, 170 (2d Cir.) (internal quotation marks omitted), cert. denied, 555 U.S. 1020, 129 S.Ct. 589, 172 L.Ed.2d 444 (2008); see, e.g., United States v. Sash, 396 F.3d 515, 521 (2d Cir. 2005).

Where there is “no procedural unreasonableness in sentencing, our review of a claim of substantive unreasonableness is narrow, akin to review for abuse of discretion.” Norman, 776 F.3d at 85; see Gall, 552 U.S. at 46, 128 S.Ct. 586. In conducting such review, we “will, of course, take into account the totality of the circumstances,” id. at 51, 128 S.Ct. 586, “ ‘evaluating] the length of the sentence imposed in light of the factors enumerated under 18 U.S.C. § 3553(a),’ ” Norman, 776 F.3d at 86 (quoting United States v. Ahders, 622 F.3d 115, 119 (2d Cir. 2010)). Under that section, the court must impose a sentence that is, inter alia, “sufficient, but not greater than necessary, to comply ■with” the variety of purposes laid out in § 3553(a)(2), including “the need for the sentence imposed ... to reflect the seriousness of the offense,” 18 U.S.C. § 3553(a)(2)(A), and “to protect the public from further crimes of the defendant,” id. § 3553(a)(2)(C). Our review of the sentencing court’s application of the § 3553(a) factors is highly deferential:

[W]e will not substitute our own judgment for the district court’s on the question of what is sufficient to meet the § 3553(a) considerations in any particular case. See United States v. Fernandez, 443 F.3d 19, 27 (2d Cir.2006). We will instead set aside a district court’s substantive determination only in exceptional cases where the trial court’s decision cannot be located within the range of permissible decisions.

Cavera, 550 F.3d at 189 (emphasis in original; internal quotation marks omitted); see also Norman, 776 F.3d at 86.

B. Tejada

The PSR prepared on Tejada, grouping his various robbery conspiracy, narcotics conspiracy, and obstruction-of-justice offenses as required by the Guidelines, calculated that his total offense level (after a recommended two-step reduction for minor role in the drug conspiracy) was 42. As his criminal history category was I, his advisory-Guidelines-recommended range was 360 months’ to life imprisonment. The PSR noted that the statutory maximum punishment for each of his counts of conviction was 20 years. The components of the PSR’s Guidelines calculation included the total amount of drugs for which Tejada was accountable in the narcotics conspiracy, see Guidelines § 2Dl.l(a)(5), and separate offense-level determinations for four robberies or attempted robberies at which Tejada was actually present, as well as two robberies at which he was not present but for which he provided police equipment. There were several enhancements with respect to each of the six robbery-related incidents, including a two-step increase for abuse of a position of public trust for each incident, see id. § 3B1.3; a two-step increase for obstruction of justice for each incident, see id. § 3C1.1; a five-step increase for brandishing or possessing a firearm in four of the incidents, see id. § 2B3.1(b)(2)(C); and increases of various size based on the quantities of drugs seized or expected to be seized in each robbery or attempted robbery, see id. § 2B3.1(b)(7).

Tejada raised multiple objections to the PSR’s findings, based principally on his contention that the evidence was insufficient to support his conviction of any of the offenses of which he had been found guilty. For example, he contended that the trial evidence was insufficient to establish that he had personally participated in, or aided and abetted, any of the robberies, and he argued that at the very least he should receive a downward adjustment for having a minor role in the robbery conspiracy (as well as the PSR’s recommended minor-role reduction with respect to the drug conspiracy). By Tejada’s calculation, his resulting advisory-Guidelines-recommended range should have been 27 to 33 months’ imprisonment.

The district court rejected Tejada’s contentions, adopting the PSR’s factual findings and stating as follows:

I credited the testimony of the accomplices. I credited the government’s evidence with regard to the use of firearms; including by the defendant himself with regard to the loss amounts. I credit the evidence in its entirety. ■
As for the historical facts that are challenged, such as his participation in particular robberies, I reject those challenges. I credit the testimony of the Government witnesses and find by a preponderance of the evidence that he has participated in these robberies to the degree and in the manner the witnesses testified to.

(T.S.Tr. 12-14.) The court sentenced Teja-da principally to 216 months’, i.e., 18 years’, imprisonment.

On appeal, Tejada contends that his sentence was procedurally unreasonable, arguing principally that the district court sentenced him largely for participating in robberies at which he was not physically present and for a firearm offense of which the jury found him not guilty. Given the district court’s permissible credibility findings, these contentions have no merit.

“Because the quantum of proof required for a verdict of guilt is higher than the quantum required for sentencing, it is established that ‘a jury’s verdict of acquittal does not prevent the sentencing court from considering conduct underlying the acquitted charge, so long as that conduct has been proved by a preponderance of the evidence.’ ” United States v. Delva, 858 F.3d 135, 160 (2d Cir. 2017) (quoting United States v. Watts, 519 U.S. 148, 157, 117 S.Ct. 633, 136 L.Ed.2d 554 (1997)); see also United States v. Vaughn, 430 F.3d 518, 527 (2d Cir. 2005) (“[D]istrict courts may find facts relevant to sentencing by a preponderance of the evidence, even where the jury acquitted the defendant of that conduct....”), cert. denied, 547 U.S. 1060, 126 S.Ct. 1665, 164 L.Ed.2d 405 (2006).

In light of the evidence discussed in Part IV above, we see no error in the ■district court’s rulings. There was ample evidence from which the jury could infer beyond a reasonable doubt that Tejada was present at the various robberies or attempted robberies described by Tineo and other cooperating witnesses. And there was ample evidence from which the court could find by a preponderance of the evidence that Tejada either brandished or carried a gun at the robberies or robbery attempts at which he was present.

Nor do we see any ground for concluding that the district court’s sentence of 18 years’ imprisonment fell outside the range of permissible decisions. In considering the § 8553(a) factors, the district court noted that “there is a lot to be said about [Tejada] on the positive side of the ledger” (T.S.Tr. 47), noting the support he had received from his family and his exemplary conduct in jail while awaiting trial, and it weighed those considerations against the fact that Tejada’s conduct constituted a “horrific betrayal of public trust” (id. at 48). Although the government urged, the court to impose sentences for some of Tejada’s offenses consecutively, in order to reach a 30-year prison term, the court concluded that that sentence would be “greater than necessary to fulfill the goals of punishment in 3553(a)(2)” (T.S.Tr. 51). Citing the “princip[al] aggravating factor” as “the fact that these crimes were committed by a police officer and that they were violent crimes” (id.), the court sentenced Tejada to 18 years’ imprisonment. On this record, we see no procedural or substantive error in Tejada’s sentence.

C. Fiorentino

Fiorentino was sentenced principally to 264 months’ imprisonment. The district court had calculated that his Guidelines-recommended range of imprisonment was 324 to 405 months. Although Fiorentino objected to that calculation in the district court, he does not argue on appeal that his sentence was infected by procedural error. Rather, he contends that his sentence was substantively unreasonable, arguing principally that it far exceeds both the mean and median prison terms of other defendants sentenced for robbery and drug trafficking crimes nationwide, and that it exceeds the sentences imposed on most of his coconspirators. We are unpersuaded.

While the sentencing court is required to consider “the need to avoid unwarranted sentence disparities among defendants with similar records who have been found guilty of similar conduct,” 18 U.S.C. § 3553(a)(6), “a reviewing court’s concern about unwarranted disparities is at a minimum when a sentence is within the Guidelines range,” United States v. Irving, 554 F.3d 64, 76 (2d Cir. 2009) (internal quotation marks omitted); see Gall, 552 U.S. at 54, 128 S.Ct. 586. Here, the sentence challenged by the defendant is well below the advisory Guidelines range, and the record reveals no abuse of discretion in the district court’s consideration of any of the § 3553(a) factors.

The court noted, inter alia, the extensive scope and duration of the conspiracy, its operation in an organized fashion over an extended period of time, Fiorentino’s own extreme violence against one victim, and the fact that “the business of robbing drug dealers intrinsically endangers everyone,” as it carries “the potential for violence that could extend beyond the immediate participants in the robbery” (Fiorentino Sentencing Transcript at 57). The court also found Fiorentino’s crimes to be more serious than the average or median crime. Despite these findings, and despite the calculated Guidelines imprisonment range of 324 to 405 months, the court sentenced Fiorentino to 264 months. Given the evidence as to Fiorentino’s crimes (see Part II above) and the district court’s assessment of the record, we cannot conclude that the district court was required to impose a prison term that was even shorter.

CONCLUSION

We have considered all of defendants’ arguments on these appeals and have found them to be without merit. The judgments are affirmed.  