This case, which is before us for a second time, see Mackler Prods., Inc. v. Cohen, 146 F.3d 126 (2d Cir.1998) (“Mackler II”), requires us to clarify further the troublesome law concerning sanctions. Frank R. Cohen, an attorney, appeals from an order of the United States District Court for the Southern District of New York (Robert P. Patterson, Judge), entered on October 22, 1999, imposing on him and one of his clients jointly and severally a “punitive” sanction of $2000 and a “compensatory” sanction of $45,000. We conclude, as we did in the previous appeal, that the District Court erred in imposing the “punitive” sanction on Cohen without providing the procedural protections employed in the criminal process. In addition, we hold that the District Court failed to give Cohen adequate notice with respect to one of the grounds on which the “compensatory” sanction was imposed. For these reasons and others explained below, we reverse the judgment in part, vacate it in part, and remand the cause for still further proceedings consistent with this opinion.
I.
Most of the facts relevant to this appeal were summarized in our previous opinion, see Mackler II, 146 F.3d at 127-28, familiarity with which is assumed, and will be restated here only to the extent necessary. In July 1992, plaintiff Mackler Productions, Inc. (“Mackler”) filed a complaint in the District Court against defendants Turtle Bay Apparel Corp. (“Turtle Bay”), Gotham Apparel Corp. (“Gotham Apparel”), Ron Pat Printing, Inc. (“Ron Pat Printing”), Michael Kipperman (“Kipperman”), Patricia Kipperman, and James J. Clare. Mackler alleged that defendants, three of whom were represented by Cohen, owed Mackler $69,090 “for goods sold and delivered ... to the defendants on or about August and September of 1989.” Specifically, Mackler contended that: (1) Turtle Bay or its principal, Kipperman, had ordered $69,090 worth of sweatshirts from-Mackler; (2) they had instructed Mackler' to deliver the merchandise to Ron Pat Printing; (3) Mackler had done so; but (4) defendants never paid for the merchandise.
As the case progressed, Mackler developed a theory of recovery against defendants based on the contention that some or all of them had owned or controlled Turtle Bay. (Turtle Bay itself was apparently defunct and had defaulted.) Mackler alleged that defendants had used Turtle Bay as part of a scheme to defraud Mackler by having the sweatshirts delivered to Ron Pat Printing and then converting the sweatshirts to defendants’ use without paying Mackler. Thus, when a non-jury trial commenced before the District Court in June 1993 (against all defendants other than Clare, who was dropped from the lawsuit on Madder’s consent, see Mackler II, 146 F.3d at 127 n. 1), Madder’s claims turned at least in part on establishing the facts surrounding the receipt and subsequent disposition of the sweatshirt shipment from Mackler and the various ownership and operating relationships among the individual and corporate defendants.
To the extent relevant here, two defense witnesses testified to these matters at the trial. First, Ronald Hoffman, who was an employee — and perhaps a part-owner' — of Ron Pat Printing, testified that he had received and signed for the Mackler shipment and that the shipment was subsequently passed on to Turtle Bay. Hoffman also testified about the ownership and control of Turtle Bay and Ron Pat Printing, stating, inter alia, that Kipperman “was just sales” at Turtle Bay and “had nothing to do with any designing or anything like *140that.” Second, Kipperman himself testified about his and his family’s relationships to various business entities, including Ron Pat Printing and Turtle Bay. In particular, he testified that: (1) Turtle Bay was owned by one David Jacobs and his brother (together, the “Jacobses”); (2) Clare (who is Kipperman’s father-in-law) did not have an equity interest in Turtle Bay; and (3) he himself was “just a sales agent,” and not a principal, of Turtle Bay. As part of its rebuttal case, Maekler offered testimony and other evidence that tended to contradict both Hoffman’s and Kipperman’s assertions.
At the close of the evidence, the District Court entered findings of fact in favor of Maekler and against defendants Gotham Apparel and Kipperman, and awarded Maekler compensatory damages of $69,090 plus interest. In addition, the District Court stated that it was referring the issue of whether Hoffman had committed perjury to the United States Attorney’s Office for possible criminal investigation and, following such investigation, would consider whether to impose any sanctions on defendants and/or their counsel. Thereafter, the District Court awarded Maekler punitive damages of $69,090, see Maekler Prods., Inc. v. Turtle Bay Apparel Corp., No. 92 Civ. 5745, 1994 WL 267857, at *2 (S.D.N.Y. June 14, 1994), and entered final judgment in Madder’s favor. By summary order dated January 11, 1995, we affirmed this judgment. See Mackler Prods. v. Turtle Bay Apparel, 47 F.3d 1158 (2d Cir.1995) (table).1
On September 18, 1996, following an investigation by the United States Attorney’s Office, Hoffman pleaded guilty to criminal perjury charges. Then, beginning on October 8, 1996, the District Court held an evidentiary hearing with respect to whether sanctions should be imposed on any defendants or on defense counsel, taking testimony from, among others, attorney Cohen and Hoffman. (Kipperman was called to testify, but invoked the Fifth Amendment.) Relying on its inherent authority, the District Court filed an Opinion and Order on May 21, 1997 imposing on Cohen and his client, Kipperman, jointly and severally a $10,000 “punitive” sanction payable to the Court and a $45,000 “compensatory” sanction payable to Mackler. See Mackler Prods., Inc. v. Turtle Bay Apparel Corp., No. 92 Civ. 5745, 1997 WL 269505, at *16 (S.D.N.Y May 21, 1997) (“Maekler I ”). The District Court based these sanctions on three factual findings: (1) that Cohen and Kipperman had caused Hoffman to present false evidence in an effort to disassociate Kipperman from responsibility for the order of sweatshirts from Maekler and the delivery of the sweatshirts to Ron Pat Printing; (2) that Kipperman gave false testimony, with Cohen’s knowledge, to the effect that Turtle Bay was owned by the Jacobses and that Clare had no equity interest in the company; and (3) that Kipperman gave false testimony, again with Cohen’s knowledge, to the effect that he himself had no interest in Turtle Bay or in Ron Pat Printing. See id. at *13-16.
Cohen filed a timely notice of appeal from the sanctions order and, by opinion dated June 22, 1998, we vacated and remanded for further proceedings. See Maekler II, 146 F.3d at 130-31. With respect to the “punitive” sanction, we held that a $10,000 punitive sanction imposed on an individual requires the procedural protections appropriate to a criminal case. See id. at 128-30. We therefore vacated the sanction and remanded “so that the district court [could] consider reimposing it after giving Cohen the benefit of procedural protections employed in the criminal process.” Id. at 130. With respect to the “compensatory” sanction, we identified two flaws requiring further proceedings. First, noting that “Cohen was entitled to *141notice of the threatened imposition of the sanction and an opportunity to be heard,” we found “no adequate indication” in the record that Cohen had received such notice. Id. Second, we concluded that the District Court based its findings with respect to Kipperman’s testimony, and Cohen’s knowledge thereof, “on inconsistent and inadequately supported reasoning.” Id. We therefore remanded “for further consideration.” Id. at 131.
On remand, the District Court did not conduct any further proceedings. Instead, by Opinion and Order filed October 22, 1999, the District Court reimposed both “punitive” and “compensatory” sanctions on Cohen and Kipperman. See Mackler Prods., Inc. v. Turtle Bay Apparel Corp., No. 92 Civ. 5745, 1999 WL 961987 (S.D.N.Y. Oct.21, 1999) (“Mackler IIP’). First, noting its disagreement with the Court of Appeals “as to what amount of punitive sanctions should invoke the protections afforded to defendants in criminal cases,” the District Court reduced the “punitive” sanction to be payable to the Court from $10,000 to $2000. Id. at *1. Second, reviewing the record, the District Court held that, contrary to our conclusion in Mackler II, 146 F.3d at 130, Cohen had, in fact, received adequate notice of the threatened imposition of the “compensatory” sanction — in the form of a memorandum on sanctions from Mackler dated April 5, 1994 and during the sanctions proceedings themselves. See Mackler III, 1999 WL 961987, at *2. Finally, quoting from its opinion in Mackler I, the District Court concluded that there was adequate, factual support for its previous findings that Kipperman had testified falsely at trial. See id. at *2-3. Nevertheless, the District Court concluded that there was in adequate support for its previous finding that Cohen had been aware of Kipper-man’s false testimony concerning Kipper-man’s ownership interest, or lack thereof, in Turtle Bay. See id. at *3-4. Accordingly, the District Court “modified” its Opinion and Order of May 21, 1997 “in that respect,” and reimposed a “compensatory” sanction of $45,000 jointly and severally on Cohen and Kipperman. See id. at *4. This appeal followed.2
II.
On appeal, Cohen principally argues: (1) that the District Court again erred in imposing the “punitive” sanction on him without employing the procedural protections appropriate to a criminal trial; (2) that he did not, in fact, receive adequate notice with respect to the possibility of a “compensatory” sanction; (3) that the “factual underpinnings” of the “compensatory” sanction remain “unsupported”; and (4) that the District Court erred in fixing the amount of the “compensatory” sanction. We review for abuse of discretion all aspects of the District Court’s decision to impose sanctions. See, e.g., Revson v. Cinque & Cinque, P.C., 221 F.3d 71, 78 (2d Cir.2000). This standard of review, however, “is not as simple as it may appear at first blush.” Schlaifer Nance & Co. v. Estate of Warhol, 194 F.3d 323, 333 (2d Cir.1999). First, the District Court “necessarily abuses its discretion if its conclusions are based on an erroneous determination of law or on clearly erroneous factual findings.”- Revson, 221 F.3d at 78 (citing Cooter & Gell v. Hartmarx Corp., 496 U.S. 384, 405, 110 S.Ct. 2447, 110 L.Ed.2d 359 (1990)). Second, “although the decision to impose sanctions ... ‘is uniquely within the province of a district court, we nevertheless need to ensure that any such decision is made with restraint and discretion.’ ” Salovaara v. Eckert, 222 F.3d 19, 26-27 (2d Cir.2000) (quoting Schlaifer Nance, 194 F.3d at 334).
A. The “Punitive” Sanction
First, we must decide whether, in light of our holding in Mackler II, the *142District Court erred in imposing the $2000 “punitive” sanction without giving Cohen the benefit of “the procedural protections appropriate to a criminal case.” 146 F.3d at 130. Such protections include notice, the opportunity to be heard, the right to a public trial, the assistance of counsel, the presumption of innocence, the privilege against self-incrimination, and the requirement of proof beyond a reasonable doubt. See id. at 128.
As noted above, we held in Mackler II that the District Court erred in imposing the $10,000 “punitive” sanction on Cohen without employing such procedures. See id. at 129. Relying principally oh International Union, United Mine Workers of America v. Bagwell, 512 U.S. 821, 827-38, 114 S.Ct. 2552, 129 L.Ed.2d 642 (1994), in which the Supreme Court discussed the distinctions between criminal and civil contempt, we reasoned that several factors supported the conclusion that Cohen was entitled to criminal procedure protections:
The sanction was not intended to be compensatory; indeed, the court imposed it in addition to a compensatory sanction and explicitly labelled it as punitive. The imposition was retrospective, by reason of past wrongful conduct; it did not seek to coerce future compliance, and no opportunity to purge was provided. The sanction was payable to the court, rather than to the injured party, further confirming its punitive nature. And the size of the required payment was substantial.
Mackler II, 146 F.3d at 129. Without addressing “a court’s ability to levy a modest punitive sanction without the protection of criminal procedures,” id. at 130 n. 2 (emphasis added); see also infra note 3, we therefore held “that the imposition of a $10,000 punitive sanction on an individual ... requires such protections,” id. at 130.
Mindful of the fact that only the size of the sanction at issue in this case has changed, we conclude, as we did in the previous appeal, that the District Court erred in imposing the “punitive” sanction on Cohen without employing the procedures appropriate to a criminal trial. The gravamen of our analysis in Mackler II— and of the Supreme Court’s analysis in Bagwell, on which we relied heavily — was whether or not the sanction at issue was criminal or civil in character. See Mackler II, 146 F.3d at 128-30; see also Bagwell, 512 U.S. at 827, 114 S.Ct. 2552 (“[Wjhether a contempt is civil or criminal turns on the ‘character and purpose’ of the sanction involved.”); id. at 828, 114 S.Ct. 2552 (“[Cjonclusions about the civil or criminal nature of a contempt sanction are properly drawn ... from an examination of the character of the relief itself.” (citations and internal quotation marks omitted) (emphases added)). Although we concluded that the size of a sanction is one factor to be weighed in making this determination, we plainly held that whether a sanction should be treated as criminal or civil in nature turns on several factors, including whether the sanction is intended to be compensatory or punitive; whether it is payable to the court or to the injured party; whether it is based on past wrongful conduct or is intended to coerce future compliance; and whether any opportunity to purge the sanction is provided. See Mackler II, 146 F.3d at 129; see also Margo v. Weiss, 213 F.3d 55, 62 (2d Cir.2000) (emphasizing some of the factors, other than size, on which we relied in Mackler II); cf. Satcorp Int’l Group v. China Nat’l Silk Import & Export Corp., 101 F.3d 3, 6 n. 1 (2d Cir.1996) (discussing the civil-criminal fine distinction without reference to the size of the fine). Here, for the reasons we stated in Mackler II, 146 F.3d at 129, all of these other factors support the conclusion that the “punitive” sanction at issue in this case is criminal in nature. Thus, notwithstanding the reduction of the sanction from $10,000 to $2000, we hold that the District Court erred in denying Cohen the procedural protections *143appropriate to a criminal case.3
Normally, having decided that the District Court committed a procedural error like the one in this case, we would remand for further proceedings, as we did in Mackler II. See 146 F.3d at 130-31. Under the circumstances of this case, however, we conclude that remand is unnecessary and inappropriate. Cohen, a 78-year-old lawyer with an apparently unblemished record until this case, has effectively been “punished” for whatever misconduct he committed by the length and nature of these proceedings, with their inevitable financial and personal cost. In our view, to impose additional monetary sanctions on him would therefore serve no useful retributive or deterrent purpose. Accordingly, exercising our supervisory powers over the administration of justice and the federal courts within this Circuit, see, e.g., In re International Business Machs. Corp., 45 F.3d 641, 645 (2d Cir.1995), we reverse the “punitive” sanction rather than vacating and remanding for the District Court to consider yet again whether the sanction should be imposed.
B. The “Compensatory” Sanction
As noted, the District Court also reimposed on remand a “compensatory” sanction of $45,000 on Cohen. This sanction was based on two factual findings: (1) that Cohen (with Kipperman) had caused Hoffman to present false evidence in an effort to disassociate Kipperman from responsibility for the order of sweatshirts from Mackler and the delivery of the sweatshirts to Ron Pat Printing; and (2) that Cohen knew of, and failed to remedy, Kip-perman’s false testimony that Turtle Bay was owned by the Jacobses and that Clare had no equity interest in the company. See Mackler III, 1999 WL 961987, at *2-4.4 On appeal, Cohen argues that the District Court failed to give him adequate notice before imposing the “compensatory” sanction, erred in concluding that the sanction was warranted on the merits, and abused its discretion in fixing the amount *144of the sanction. We address these arguments in turn.
1. Notice
It is well established that “[d]ue process requires that courts provide notice and an opportunity to be heard before imposing any kind of sanctions.” Ted Lapidus, S.A v. Vann, 112 F.3d 91, 96 (2d Cir.1997) (internal quotation marks omitted) (emphasis added). “The purpose of particularized notice is to put counsel on notice as to the particular factors that he must address if he is to avoid sanctions.” Id. (internal quotation marks omitted). Thus, “[a]t a minimum, the notice requirement mandates that the subject of a sanctions motion be informed of: (1) the source of authority for the sanctions being considered; and (2) the specific conduct or omission for which the sanctions are being considered so that the subject of the sanctions motion can prepare a defense.” In re 60 E. 80th St. Equities, Inc., 218 F.3d 109, 117 (2d Cir.2000).
Applying these principles to the present case, it is plain that Cohen received adequate notice with respect to the possibility of sanctions on the ground that he had caused Hoffman to present false evidence. On April 5, 1994, Mackler circulated a Memorandum Regarding a Hearing on Sanctions (the “April 5, 1994 Memorandum”), which invoked, inter alia, the District Court’s inherent power and argued that the Court should impose sanctions on Cohen for “aid[ing] in preparing Ron Hoffman’s perjured testimony.”5 Additionally, the record reflects that Cohen was present on October 8, 1996, when the District Court held a hearing on possible sanctions and heard testimony from Hoffman about his perjured testimony at trial. Finally, on November 4, 1996, several weeks before three days of hearings on sanctions, the District Court held a conference with counsel for all parties facing possible sanctions — including counsel for Cohen — at which the District Court limited the issues to possible sanctions against Kipperman and Cohen for “the lying of Ron Hoffman” and “any lying with respect to Kipperman’s relationship to Turtle Bay.” Together, these forms of notice are more than enough to satisfy the due process requirement.
Nevertheless, we conclude that the District Court failed to give Cohen adequate notice with respect to the possibility of sanctions on the ground that he had known of, but failed to remedy, Kipper-man’s false testimony concerning the ownership interests in Turtle Bay of the Ja-cobses and Clare. Mackler’s April 5, 1994 Memorandum did not raise these particular allegations of wrongdoing. Nor did the District Court mention them at the October 8, 1996 hearing or the November *1454, 1996 conference. Rather, to the extent that Cohen received notice in connection with Kipperman’s testimony, he was notified only that he faced sanctions with respect to Kipperman’s false testimony about Kipperman’s own ownership interests in Turtle Bay, not those of the Ja-cobses or Clare. Thus, with respect to the testimony concerning the Jacobses and Clare, Cohen was deprived of the “particularized, notice” to which he was entitled, Ted Lapidus, 112 F.3d at 96 (emphasis added), and, insofar as the “compensatory” sanction was imposed on this basis, it cannot stand. Cf. Nuwesra v. Merrill Lynch, Fenner & Smith, Inc., 174 F.3d 87, 92-93 (2d Cir.1999) (vacating a sanction where the appellant attorney was warned about possible sanctions in connection with “conduct leading up to and including the filing of the complaint” because the sanctions were based in part on other conduct, with respect to which the appellant received no notice); Ametex Fabrics, Inc. v. Just In Materials, Inc., 140 F.3d 101, 109 (2d Cir.1998) (“Absent a statement from the district court explicitly informing [the appellant attorney] that it was considering sanctions against him for making false representations on October 5, 1995 to that court, [the attorney] was entitled to assume that the court was considering sanctions only for the entirely separate act of filing the ... action in bad faith.”).6
2. The Merits
Having concluded that the notice of possible sanctions was partially inadequate, we need consider the merits only of the District Court’s decision to impose sanctions with respect to Cohen’s role in Hoffman’s presentation of false testimony. At the sanctions hearings in 1996, Hoffman testified that he had given false testimony at the 1993 trial when he claimed that he received and signed for the Mackler shipment and when he stated that Kipperman “was just sales” at Turtle Bay and “had nothing to do with any designing or anything like that.” In addition, Hoffman testified at the hearings that he, Kipperman, and Cohen “had [a] conversation about the goods” just prior to the 1993 trial, in which Cohen explicitly instructed Hoffman to testify falsely that he had received and signed for the shipment. The District Court found Hoffman’s testimony at the sanctions hearings to be credible, noting that it was “corroborated by documentary evidence,” and therefore concluded that Cohen (with Kipperman) had “caused Mr. Hoffman to present false evidence to the Court in an effort to disassociate Mr. Kip-perman and Gotham Apparel from responsibility for the order of the sweatshirts from Mackler and the delivery of the sweatshirts to Ron Pat Printing.” Mackler I, 1997 WL 269505, at *13; see also Mackler III, 1999 WL 961987, at *4 n. 7 (incorporating by reference the District Court’s findings in Mackler I concerning Cohen’s role in Hoffman’s false testimony). Mindful that the “[assessment of the credibility of witnesses is peculiarly within the province of the trier of fact and is entitled to considerable deference,” Healey v. Chelsea Resources, Ltd., 947 F.2d 611, 618 (2d Cir.1991), we cannot say that these findings of the District Court are clearly erroneous or that the District Court abused its discretion in imposing a “compensatory” sanction on this basis.
3. The Size of the Sanction
Although we conclude that the District Court did not abuse its discretion by imposing a sanction on Cohen for his role in causing Hoffman’s false testimony, we *146nevertheless vacate the “compensatory” sanction and remand for still further proceedings. We do so for two independent reasons. First, while the District Court based Cohen’s “compensatory” sanction on two factual findings — namely, that Cohen caused Hoffman to present false evidence and that Cohen knew of, and faded to remedy, Kipperman’s false testimony concerning the ownership interests in Turtle Bay of the Jacobses and Clare — we have affirmed only the first finding because of the deficiencies in the notice Cohen received.7 Accordingly, remand is necessary for the District Court to consider whether to reimpose the full $45,000 sanction on Cohen or a sanction of some lesser amount.
In addition, remand is necessary because it appears that the District Court erred in fixing the amount of the “compensatory” sanction by relying on unsworn assertions by Mackler concerning its injury. Although a party facing compensatory sanctions is not necessarily entitled to an evidentiary hearing with respect to the amount of proposed sanctions, see Schlaifer Nance, 194 F.3d at 335, due process requires, at a minimum, that: (1) the party seeking to be compensated provide competent evidence, such as a sworn affidavit, of its claimed attorney’s fees and expenses; and (2) the party facing sanctions have an opportunity to challenge the accuracy of such submissions and the reasonableness of the requested fees and expenses. See, e.g., Caisse Nationale de Credit Agricole-CNCA v. Valcorp, Inc., 28 F.3d 259, 266-67 (2d Cir.1994) (upholding the imposition of sanctions and rejecting the appellants’ argument that the appellee’s proof of fees was inadequate where the appellee had submitted an affidavit detailing the names, hourly rates, and time spent by each attorney who worked on the case); cf. Dague v. City of Burlington, 976 F.2d 801, 804 (2d Cir.1992) (noting that the amount of attorney’s fees should usually “be fixed in the first instance by the district court, after the district court hears evidence as to the extent and nature of the services rendered”); Fustok v. ContiCommodity Servs., Inc., 873 F.2d 38, 40 (2d Cir.1989) (holding that the District Court’s calculation of attorney’s fees based on an affidavit detailing the hours spent on the case “d[id] not constitute a denial of due process”). Here, it appears from a review of the record that Mackler did not submit any competent evidence of its claimed fees and expenses. Instead, the District Court apparently relied on an unsworn assertion by Mackler in its PosMIearing Memorandum on Sanctions (a document that is not listed on the' District Court’s docket sheet and could not be found in the record on appeal) that Mackler had incurred fees and expenses totaling $99,639.35. See Mackler I, 1997 WL 269505, at *16 (“[Mackler] as-serbs that it had incurred attorneys fees and expenses totaling $99,639.35 during the trial, appeal and sanctions hearing in this action (Plaintiffs Post-Hearing Memorandum on Sanctions at 2).” (emphasis added)). By relying on this unsworn assertion, and failing to provide Cohen with an opportunity to challenge the accuracy and reasonableness of Mackler’s asserted expenses, the District Court denied Cohen his right to due process of law.
III.
Finally, we grant Cohen’s request that this case be reassigned on remand to a new District Judge. As a general rule, cases remanded to a District Court for further proceedings are sent back without any directions or suggestions as to the judge before whom they are to be conducted; in most cases, such matters are “properly left to the district court.” United States v. Robin, 553 F.2d 8, 9 (2d Cir.1977) (en banc). Nevertheless, “in a few instances there may be unusual dr-*147cumstances where both for the judge’s sake and the appearance of justice,” an order of reassignment is appropriate. Id. at 9-10 (internal quotation marks and citations omitted). The principal factors to be weighed in making a determination of whether reassignment is appropriate are:
(1) whether the original judge would reasonably be expected upon remand to have substantial difficulty in putting out of his or her mind previously-expressed views or findings determined to be erroneous or based on evidence that must be rejected, (2) whether reassignment is advisable to preserve the appearance of justice, and (3) whether reassignment would entail waste and duplication out of proportion to any gain in preserving the appearance of fairness.
Id. at 10; see also Reilly v. NatWest Mkts. Group, Inc., 181 F.3d 253, 271-72 (2d Cir.1999) (relying on Robin in a civil case); Springs Mills, Inc. v. Ultracashmere House, Ltd., 724 F.2d 352, 357 (2d Cir.1983) (same). Where we have found these factors to weigh in favor of reassignment, we have often stressed that “our remand does not imply any personal criticism of the [district] judge.” Robin, 553 F.2d at 10 (discussing cases).
Although we harbor no doubt that the District Judge in this case would be able to “put[] out of his mind” any disagreements he might have with our decisions here and in Mackler II, we conclude that reassignment is appropriate in this case, “to preserve the appearance of justice.” Id. This case, which first arose in 1989, has been litigated for over eight years, and has involved two separate appeals—raising largely the same questions—on the sanctions issue alone. These circumstances, when combined with the unique nature of sanctions proceedings (in which “the offended judge [is] solely responsible for identifying, prosecuting, adjudicating, and sanctioning the contumacious conduct,” Bagwell, 512 U.S. at 831, 114 S.Ct. 2552) and the limited nature of our remand (for reconsideration of the size of the “compensatory” sanction imposed on Cohen), are “unusual” enough to depart from the general rule of sending a case back without instructions or suggestions as to assignment. In reaching this conclusion, we stress, as we have before when ordering reassignment, that “our remand does not imply any personal criticism of the [district] judge.” Robin, 553 F.2d at 10. (Indeed, in some respects, the District Judge’s decision on remand evidences his ability to reconsider previous findings adverse to Cohen. See supra note 4.) Rather, it is meant to bring this matter to an expeditious and equitable conclusion in a manner designed to avoid any question, legitimate or not, about the justice of that conclusion.
IV.
In sum, for the reasons stated above, we:
(1) REVERSE the District Court’s imposition of a $2000 “punitive” sanction on Cohen;
(2) VACATE the imposition of a $45,000 “compensatory” sanction;
(3) REMAND for the District Court to consider whether to reimpose a “compensatory” sanction of some amount on Cohen consistent with this opinion; and
(4) ORDER that on remand the case be assigned to a different District Judge.
We decline to award costs of this appeal to either party. See Fed. R.App. P. 39(a)(4).
. Pursuant to Rule 0.23 of our Court Rules, a summary order may be cited or otherwise used in a subsequent proceeding of the same case. See 2d Cir. R. 0.23; see also Baker v. Latham Sparrowbush Assocs., 72 F.3d 246, 253-54 (2d Cir.1995).
. Because Kipperman did not file a notice of appeal from the order imposing sanctions, Cohen is the sole appellant.
. In arguing that the “punitive” sanction should be affirmed, Mackler relies heavily on our statement in Mackler II that “[w]e do not address a court’s ability to levy a modest punitive sanction without the protection of criminal procedures.” 146 F.3d at 130 n. 2. As an initial matter, this statement was plainly dictum, since the sole question presented in Mackler II was whether the District Court had erred in imposing the $10,000 "punitive” sanction without the protections of criminal procedures. Moreover, nothing in our statement, which was relegated to a footnote, contradicts the holding that whether criminal procedures are required turns on whether a sanction is criminal or civil in nature, which itself turns on several different factors.
As in Mackler II, we do not address here whether a court may impose a more modest punitive sanction without the protections of criminal procedure because any such discussion would itself be dictum. We merely decide that, when viewed in light of the other relevant factors, the $2000 “punitive” sanction at issue in this case could not be imposed without such protections. Cf. Bagwell, 512 U.S. at 829, 114 S.Ct. 2552 ("[A] flat, unconditional fine totaling even as little as $50 announced after a finding of contempt is criminal if the contemnor has no subsequent opportunity to reduce or avoid the fine through compliance.” (internal quotation marks omitted)).
. As noted above, see supra at 140-41, the District Court originally imposed the "compensatory” sanction on Cohen based on three factual findings: (1) that Cohen (with Kipper-man) had caused Hoffman to present false evidence; (2) that Cohen knew of, and failed to remedy, Kipperman’s false testimony concerning the ownership interests of the Jacobs-es and Clare in Turtle Bay; and (3) that Cohen knew of, and failed to remedy, Kipper-man’s false testimony concerning Kipper-man's own interests in Turtle Bay and Ron Pat Printing. See Mackler I, 1997 WL 269505, at *14-16. The District Court in Mackler III reimposed the “compensatory” sanction on Cohen in based only on the first two of its original findings, having concluded that Cohen might not have known of Kipper-man’s false testimony concerning Kipper-man's own interests in Turtle Bay and Ron Pat Printing. See Mackler III, 1999 WL 961987, at *3-4. Accordingly, the District Court's finding that Kipperman testified falsely about his own relationships to Turtle Bay and Ron Pat Printing is not at issue in this appeal.
. In Madder II, we found "no adequate indication” that the April 5, 1994 Memorandum "was timely delivered to Cohen,” based in part on Cohen’s representation that he did not receive the memorandum. See Brief for Appellant, No. 97-7789, at 1 ("[Cohen] was given no formal notice of the charges he faced. The first ‘suggestion’ he received [of possible sanctions] ... was communicated, and then only implicitly, only after the hearing began.” (emphasis in original)); see also Reply Brief for Appellant, No. 97-7789, at 1-4 (pointing out that the affidavit of service states that Mackler’s memorandum was delivered to Cohen’s successor counsel, not to Cohen). In finding no such indication, however, we overlooked a letter dated May 2, 1994 from Cohen to the District Court responding in detail to the allegations set forth in Mack-ler's memorandum. See ROA # 79. In light of this letter, it is beyond dispute that Cohen timely received the April 5, 1994 Memorandum.
Although Cohen now concedes that he "apparently did receive [Mackler’s] memorandum and responded in part,” he nevertheless argues that he was entitled to more "formal” notice of some sort. Brief of Appellant at 15. This argument is plainly without merit. See, e.g., 60 East 80th Street Equities, 218 F.3d at 118 (noting that "while ordinarily it is preferable for a court to provide an attorney with advance, written notice of the possibility of sanctions,” we have not always required such formal notice (citing New York v. Operation Rescue Nat'l, 80 F.3d 64, 72-73 (2d Cir.1996))).
. It could be argued that the defect in notice was cured insofar as the sanction at issue here was imposed on remand and, by then, Cohen was aware of the specific allegations concerning Kipperman's false testimony. However, we need not, and do not, consider this argument, because Mackler failed to raise it both before the District Court and on appeal. See, e.g., Gibeau v. Nellis, 18 F.3d 107, 109 (2d Cir.1994) (“Where a party has failed to raise an argument in the district court, an appellate court may only consider the argument where necessary to serve an interest of justice.” (internal quotation marks omitted)).
. It should be recalled that the "compensatory” sanction imposed on Cohen in Mackler I was based on three different factual findings, one of which was discarded by the District Court in Mackler III. See supra note 4.