
528 F.3d 157 (2008)
UNITED STATES of America, Appellee,
v.
Michael BRUMER and Lawrence Klein, Defendants-Appellants.
Docket Nos. 07-0715-cr(L), 07-0716-cr(con).
United States Court of Appeals, Second Circuit.
Argued: May 29, 2008.
Decided: June 10, 2008.
*158 John W. Mitchell, New York, NY, for Defendants-Appellants.
Robin W. Morey, Assistant United States Attorney (Marcus A. Asner, Celeste L. Koeleveld, Assistant United States Attorneys, on the brief), for Michael J. Garcia, United States Attorney for the Southern District of New York, New York, NY, for Appellee.
Before: JACOBS, Chief Judge, CALABRESI and SACK, Circuit Judges.
PER CURIAM:
Michael Brumer and Lawrence Klein appeal from judgments entered in the United States District Court for the Southern District of New York (Wood, J.) on January 12, 2007, convicting them, after guilty pleas, of conspiracy to commit mail fraud, health care fraud and making false statements relating to health care matters, in violation of 18 U.S.C. §§ 371, 1341, 1347 and 1035; health care fraud, in violation of 18 U.S.C. §§ 1347 and 2; and conspiracy to violate the Medicare anti-kickback statute, 42 U.S.C. §§ 1320a-7b(b)(1) and 1320a-7b(b)(2), in violation of 18 U.S.C. § 371.

I.
On appeal, defendants seek to withdraw their guilty pleas principally on the ground that the government breached the plea agreements' provision requiring the parties to forbear from offering certain sentencing arguments. The government argued for sentence enhancements based on vulnerable victims and use of mass marketing, but claims it did so only in response to a breach by defendants, who sought a Fatico hearing on the intended loss amount. We review plea agreements de novo and in accordance with principles of contract law. United States v. Griffin, 510 F.3d 354, 360 (2d Cir.2007). "To determine whether a plea agreement has been breached, we `look[ ] to the reasonable understanding of the parties as to the terms of the agreement.'" United States v. Riera, 298 F.3d 128, 133 (2d Cir.2002) (quoting United States v. Colon, 220 F.3d 48, 51 (2d Cir.2000)). "When the Government breaches a plea agreement, the defendant is entitled to either withdraw his plea or have his agreement specifically performed." United States v. Cimino, 381 F.3d 124, 127 (2d Cir.2004).
The plea agreements provided that "neither party will seek [a downward or an upward] departure or seek any adjustment *159 not set forth herein. Nor will either party suggest that the Probation Department consider such a departure or adjustment, or suggest that the Court sua sponte consider such a departure or adjustment." As a result of developments arising out of the trial of Brumer's and Klein's co-defendants, the government offered to reduce the intended loss amount from the range set forth in Brumer's and Klein's plea agreements ($10 million to $20 million) to $5 million to $10 million. In so doing, the government conducted itself in a way that reflected a commitment to a fair outcome; its offer to amend the plea agreements to benefit defendants was not a material breach of those agreements. See New Windsor Volunteer Ambulance Corps, Inc., v. Meyers, 442 F.3d 101, 117 (2d Cir.2006) (quoting Callanan v. Powers, 199 N.Y. 268, 284, 92 N.E. 747, 752 (1910), for the proposition that a breach is material only if it is "`so substantial and fundamental as to strongly tend to defeat the object of the parties in making the contract.'").
Brumer and Klein rejected the offer to amend the plea agreements, advised the district court that the intended loss amount was in dispute, and thereafter requested (and obtained) a Fatico hearing on that issue. At the Fatico hearing, the government lost the benefit of its bargain by being put to its proof. The result was a significantly lower loss amount with a corresponding impact on the ultimate sentence. Defendants thus materially breached the plea agreements, and having done so, relieved the government of its obligations to comply with them. See United States v. Byrd, 413 F.3d 249, 251 (2d Cir. 2005) (per curiam) ("When the defendant is the party in breach, the government is entitled to specific performance of the plea agreement or to be relieved of its obligations under it.").
The government was within its rights to treat the plea agreements as unenforceable following the defendants' material breach, and specifically to seek sentence enhancements other than those stipulated. See Cimino, 381 F.3d at 128 & n. 3 (concluding that defendant's breach of sentence advocacy prohibition gave government the option of canceling plea agreement or being excused from its reciprocal obligations); see also United States v. El-Gheur, 201 F.3d 90, 93-94 (2d Cir.2000) (holding that defendant's breach of cooperation agreement absolved the government of obligation to move for downward departure pursuant to U.S.S.G. § 5K1.1); United States v. Merritt, 988 F.2d 1298, 1313 (2d Cir.1993) ("[A] defendant who materially breaches a plea agreement may not claim its benefits." (citations omitted)). Under the circumstances of this case, the government's sentence advocacy in contradiction of the plea agreements did not entitle defendants to withdraw their pleas.
The district court reached the same conclusion by a different route. The district court ruled that defendants' request for a Fatico hearing was not a breach, and that the government's sentence advocacy, if in breach, was moot because the court did not consider it. As a result, the district court imposed a sentence that relied on the lower loss amount established at the Fatico hearing. The government has not appealed the district court's ruling on breach, and therefore does not seek specific performance of defendants' obligations under the plea agreements. Accordingly, although we disagree with the district court's ruling on breach, we affirm the convictions and sentences imposed.

II
Brumer and Klein further argue they are entitled to withdraw their pleas because *160 of procedural defects in the acceptance of their pleas, which were conducted by a magistrate judge with defendants' consent.
First, defendants argue that the district judge erred when, outside their presence, she reviewed their plea allocutions and signed the orders accepting those pleas. Section 636(b)(3) of the Federal Magistrates Act permits defendants to consent (as these defendant did) to entry of their guilty pleas in front of a magistrate judge. See 28 U.S.C. § 636(b)(3) (permitting assignment of "such additional duties as are not inconsistent with the Constitution and laws of the United States"); see also United States v. Williams, 23 F.3d 629, 632-34 (2d Cir. 1994) (holding that Magistrates Act authorizes district court to refer plea allocution to magistrate provided defendant consents). Defendants do not dispute that the magistrate judge's conduct of their plea allocutions satisfied the requirements of Fed.R.Crim.P. 11(c). Having consented to this procedure, defendants were not entitled to be present when the district judge reviewed the allocution transcripts and signed the orders accepting the pleas. See United States v. Jones, 381 F.3d 114, 122 (2d Cir.2004) (right to be present "is triggered only when the defendant's `presence has a relation, reasonably substantial, to the fullness of his opportunity to defend against the charge,' and there is no constitutional right to be present `when presence would be useless, or the benefit but a shadow'" (quoting Snyder v. Massachusetts, 291 U.S. 97, 105-07, 54 S.Ct. 330, 78 L.Ed. 674 (1934))).
Second, defendants argue that the district court neglected the procedures of 28 U.S.C. § 636(b)(1) and (b)(1)(C), which require, inter alia, filing of proposed findings and recommendations with the court, mailing a copy to all parties, and providing ten days for written objections. However, these requirements apply only to delegations to a magistrate judge pursuant to § 636(b)(1). There are no similar requirements set forth under § 636(b)(3), and there is no basis for judicially engrafting such requirements onto that subsection. See Minetti v. Port of Seattle, 152 F.3d 1113, 1114 (9th Cir.1998) (per curiam) (holding that § 636(b)(3) "does not require the magistrate judge to submit proposed findings and recommendations" and "does not provide a party with ten days to file written objections with the district court").

III
Klein argues that his Sixth Amendment right to counsel was violated when the district court refused to allow him to substitute retained counsel.
"While a defendant has a right to counsel of his choice under the Sixth Amendment, it is not an absolute right. Absent a conflict of interest, a defendant in a criminal case does not have the unfettered right to retain new counsel. . . ." United States v. Paone, 782 F.2d 386, 392 (2d Cir.1986) (citations omitted). "In determining whether to allow a defendant to retain new counsel, the court must consider. . . the risks and problems associated with the delay, and whether substitutions would disrupt the proceedings and the administration of justice." Id.; see United States v. Llanes, 374 F.2d 712, 717 (2d Cir.1967) ("Judges must be vigilant that requests for appointment of a new attorney. . . should not become a vehicle for achieving delay.").
In May 2006  six years after the indictment in this case and four years after the guilty pleas  Klein sought to replace his sixth attorney with a seventh. The district court properly weighed the delay and inefficiency that might ensue and disallowed *161 formal substitution, while permitting new counsel to participate in the proceedings. In particular, the district court was concerned that without the involvement of previous counsel, a new lawyer would seek to extend the briefing schedule and would repeat arguments previously heard and rejected. We affirm that the district court's ruling was well within its discretion. See United States v. Simeonov, 252 F.3d 238, 241 (2d Cir.2001) (reviewing denial of request to substitute for abuse of discretion).
Klein contends on appeal that the district court erred by referencing a four-factor test from United States v. John Doe No. 1, 272 F.3d 116, 122-23 (2d Cir.2001), which he argues applies only to substitutions of appointed counsel, not personally retained counsel. From our reading of the transcript, however, it is clear that the district court looked to the John Doe No. 1 factors only after determining that allowing the substitution would cause substantial delay and inefficiency. Thus, only as a secondary inquiry did the district court assess whether the conflict between Klein and his then-current counsel "was so great that it resulted in a total lack of communication preventing an adequate defense," id. at 122 (internal quotation marks omitted), to ensure that any conflict was not interfering with effective representation. Although delay is generally a valid reason to deny a motion to substitute counsel, it is not necessarily valid where counsel is shown to be providing constitutionally ineffective representation. Cf. Daniels v. Woodford, 428 F.3d 1181, 1200 (9th Cir. 2005) ("Even if the trial court becomes aware of a conflict on the eve of trial, a motion to substitute counsel is timely if the conflict is serious enough to justify the delay.").
We also conclude that United States v. Gonzalez-Lopez, 548 U.S. 140, 126 S.Ct. 2557, 165 L.Ed.2d 409 (2006), does not require a different result. In that case, the government conceded that the district court erred in refusing to allow the defendant to substitute counsel, and in barring the proposed new counsel from any contact with the defendant. At issue was only whether the ruling violated the defendant's Sixth Amendment right to counsel in the absence of a finding of ineffectiveness, or prejudice to the defendant. The Court held that "[w]here the right to be assisted by counsel of one's choice is wrongly denied,. . . it is unnecessary to conduct an ineffectiveness or prejudice inquiry to establish a Sixth Amendment violation." Id. at 148, 126 S.Ct. 2557.
At the same time, the Supreme Court cautioned that the right to counsel of choice is not absolute, and is limited by "the authority of trial courts to establish criteria for admitting lawyers to argue before them." Id. at 151, 126 S.Ct. 2557. The Court "recognized a trial court's wide latitude in balancing the right to counsel of choice against the needs of fairness, and against the demands of its calendar," id. at 152, 126 S.Ct. 2557, and upheld a trial court's "power to enforce rules or adhere to practices that determine which attorneys may appear before it, or to make scheduling and other decisions that effectively exclude a defendant's first choice of counsel," id. The district court here did not exceed the latitude afforded it under Gonzalez-Lopez when the court struck the balance in favor of retaining Klein's sixth lawyer while permitting the seventh to participate.
For the foregoing reasons, the order of the district court is affirmed. The mandate shall issue forthwith.
