
    UNITED STATES of America, Appellee, v. Bernard WILLIAMS, Defendant-Appellant.
    Docket No. 04-2882-CR.
    United States Court of Appeals, Second Circuit.
    Argued: Feb. 4, 2005.
    Decided: Feb. 23, 2005.
    
      Lucas E. Andino, New York, NY. (Ivan S. Fisher, New York, N.Y., on the brief), for Defendant-Appellant.
    Michael A. Asaro, Asst. U.S. Atty., Brooklyn, N.Y. (Roslynn R. Mauskopf, U.S. Atty., Emily Berger, Asst. U.S. Atty., Brooklyn, N.Y., on the brief), for Appellee.
    Before: Before: NEWMAN and POOLER, Circuit Judges; and BRIEANT, District Judge.
    
      
       Honorable Charles L. Brieant of the United States District Court for the Southern District of New York, sitting by designation.
    
   JON 0. NEWMAN, Circuit Judge.

This appeal of a sentence imposed before the Supreme Court’s decision in United States v. Booker, — U.S. -, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), provides an opportunity to amplify our reasons for the form of remand we have used in some pending cases with sentences that are erroneous in light of Booker. See United States v. Crosby, 397 F.3d 103 (2d Cir.2005). Bernard Williams appeals from the May 19, 2004, judgment of the District Court for the Eastern District of New York (Nina Gershon, District Judge), sentencing him to 46 months’ imprisonment after a jury found him guilty of recklessly causing the transportation of hazardous materials, in violation of 49 U.S.C. § 46312(a)(2). We conclude that the sentencing judge’s mandatory use of a Sentencing Guidelines enhancement violated the Sixth Amendment and, in the circumstances of this case, warrants a Crosby remand. We therefore remand to afford the District Court an opportunity to determine whether, under Booker, the sentence originally imposed would have been materially different, and, if so, to resentence.

Background

The jury was entitled to find the following facts. In February 2002, Williams flew from Ft. Myers, Florida to New York City’s LaGuardia Airport. His checked baggage consisted of two cartons labeled “Cat’s Pride Kitty Litter,” which in fact contained thirteen or fourteen one-gallon jugs of concentrated liquid ammonia. During the flight, vapors from one of the jugs escaped into the passenger compartment, and several passengers complained about irritation. Upon his return from a trip abroad in July 2002, Williams was arrested and questioned about his prior transportation of ammonia. He admitted that he was aware that the ammonia was highly concentrated and would have to be diluted prior to use.

A grand jury indicted Williams on two counts. Count One charged that he “willfully” delivered property containing hazardous material to an air carrier for transportation in air commerce, a violation of 49 U.S.C. § 46312(a)(1). Count Two charged that he “knowingly and recklessly” caused the transportation of such property in air commerce, a violation of 49 U.S.C. § 46312(a)(2). The jury convicted Williams only on Count 2.

The District Court calculated an applicable sentencing range under the then-mandatory Sentencing Guidelines. Starting from a base offense level of 8 applicable to transportation of hazardous materials in commerce, see U.S.S.G. § 2Q1.2, Judge Gershon first added a four-level enhancement for release of hazardous gasses into the atmosphere, see id. § 2Q1.2(b)(1)(B), to which the Government and Williams had stipulated. Then, pertinent to the pending appeal, she added a nine-level enhancement for substantial likelihood of death or serious bodily injury, see id. § 2Q1.2(b)(2). The adjusted offense level of 21, in Criminal History Category I, yielded a sentencing range of 37-46 months. Defense counsel urged Judge Gershon to make a downward departure, citing 49 U.S.C. § 46312(b), which provides that knowledge of applicable regulations is not an element of an offense under section 46312(a) but “shall be considered in mitigation of the penalty.” Counsel contended that this provision authorizes a departure for a defendant who lacks knowledge of the applicable regulations. Judge Gershon appears to have accepted counsel’s reading of the statute, but declined to make a departure, stating her view that Williams had “deliberately snuck [the ammonia] on to the plane” and was “fully aware that he wasn’t permitted to transport concentrated ammonia on a passenger aircraft.” Judge Gershon’s sentence included a prison term of 46 months, a $7,500 fine, and three years of supervised release.

On appeal, Williams primarily contends that his sentence violates his Sixth Amendment rights under Blakely v. Washington, — U.S. -, 124 S.Ct. 2531, 159 L.Ed.2d 403 (2004), a ruling that Booker has now explicitly applied to the Guidelines. He also contends that the sentencing judge improperly penalized him based on a finding that was contrary to the jury’s verdict.

Discussion

1. Sixth Amendment Error

Booker, the Supreme Court made clear that a sentencing judge violates the Sixth Amendment by finding facts and mandatorily using them to enhance a sentence above the Guidelines range that would have been applicable based solely on facts found by the jury. — U.S. at -, - - -, 125 S.Ct. at 750, 755-56. The Court also implicitly ruled, by its remand of the sentence imposed on Ducan Fanfan, id. at 769, that a sentencing judge commits error by mandatorily imposing a Guidelines sentence even though it is based only on facts found by the jury.

In the pending appeal, the sentencing judge found as a fact that Williams had created a substantial likelihood of serious bodily injury or death, and, based on that finding, mandatorily made a nine-level enhancement to reach an adjusted offense level of 21. Williams’ sentence therefore violates the Sixth Amendment, just as Booker’s sentence did. See Crosby, 397 F.3d. at 109.

2. Alleged Use of “Acquitted Conduct”

Williams also contends that the sentencing judge’s finding that he had “deliberately” brought the ammonia aboard the plane, “fully aware” that this action was prohibited, was impermissibly used in determining the sentence because the finding is contrary to the jury’s acquittal on Count One, which charged “willful” conduct. In essence, he contends that the judge used “acquitted conduct,” or, perhaps more precisely, “acquitted state of mind,” in determining the sentence.

Prior to Booker, the Supreme Court had ruled that a sentencing judge could use acquitted conduct to determine a Guidelines sentence. See United States v. Watts, 519 U.S. 148, 157, 117 S.Ct. 633, 136 L.Ed.2d 554 (1997). Whether or not Watts fully survives Booker, Judge Gershon’s finding that Williams acted deliberately, by itself, provides no basis for disturbing the sentence. Even if her finding of “deliberate” action can be said to be contrary to the jury’s implicit rejection of willfulness by acquitting on Count One, use of the finding did not support any mandatory calculation under the Guidelines, nor violate any of the judge’s obligations to consider relevant factors, as required by 18 U.S.C. § 3553(a). See Crosby, 397 F.3d at 111-12. Judge Gershon used the finding as part of her reason for declining to make a discretionary departure authorized by the Guidelines, see U.S.S.G. § 2Q1.2, comment. (n.4), and properly “considered” Williams’ state of mind in declining to “mitigat[e]” the penalty, as authorized by 49 U.S.C. § 46312(b). Although the sentence in its totality is erroneous in light of Booker, this finding did not constitute or contribute to any error.

3. Form of Remand

The Courts of Appeals (or panels of them) have adopted three different responses upon review of a sentence, imposed before Booker, where an un-preserved error violates the Sixth Amendment. All three responses reckon with the plain error doctrine, but apply it in different ways, resulting in different appellate outcomes that will yield different trial court outcomes in some circumstances. Some appellate courts have remanded for resentencing. See United States v. Davis, 397 F.3d 173, 2005 WL 334370 (3d Cir. Feb.11, 2005); United States v. Oliver, 397 F.3d 369, 2005 WL 233779 (6th Cir. Feb. 2, 2005); United States v. Hughes, 396 F.3d 374, 2005 WL 147059 (4th Cir. Jan.24, 2005). Some have affirmed. See United States v. Rodriguez, 398 F.3d 1291, 2005 WL 272952 (11th Cir. Feb.4, 2005); United States v. Bruce, 396 F.3d 697, 2005 WL 241254 (6th Cir. Feb.3, 2005). Our Court has remanded for consideration by the sentencing judge of whether resentencing is needed, and, if so, to resentence. See Crosby, 397 F.3d. at 105, 117. These various responses prompt us to analyze the application of the plain error doctrine in the context of a review of sentences, assess the three responses in light of that analysis, and explain our adherence to the form of a Crosby remand.

As authoritatively set forth by the Supreme Court, the plain error doctrine permits a trial court error, not properly preserved for appeal, to warrant appellate relief when four factors are present: there must be an error, the error must be “plain,” the error must “affect[] substantial rights,” and the error must “seriously affect[] the fairness, integrity, or public reputation of judicial proceedings.” United States v. Cotton, 535 U.S. 625, 631-32, 122 S.Ct. 1781, 152 L.Ed.2d 860 (2002) (internal quotation marks omitted); see United States v. Olano, 507 U.S. 725, 731-32, 736, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993). The Court has identified these so-called “Olano ” factors as required to implement Rule 52(b) of the Federal Rules of Criminal Procedure, which now provides: “A plain error that affects substantial rights may be considered even though it was not brought to the court’s attention.” Fed.R.Crim.P. 52(b); see Olano, 507 U.S. at 731, 735-36, 113 S.Ct. 1770 (referring to pre-2002 version of Rule 52(b)). The first three Olano factors derive from the wording of Rule 52(b), a rule adopted to codify prior practice, see United States v. Frady, 456 U.S. 152, 163 n. 13, 102 S.Ct. 1584, 71 L.Ed.2d 816 (1982) (citing Fed.R.Crim.P. 52(b) advisory committee’s note). The fourth factor has also evolved from prior practice, and that evolution is instructive.

The fourth factor, as stated in Olano, 507 U.S. at 732, 113 S.Ct. 1770, is quoted verbatim from United States v. Atkinson, 297 U.S. 157, 160, 56 S.Ct. 391, 80 L.Ed. 555 (1936), a civil case tried to a jury. Atkinson indicated that the ability of appellate courts to correct unpreserved error might be greater in criminal cases:

In exceptional circumstances, especially in criminal cases, appellate courts, in the public interest, may, of their own motion, notice errors to which no exception has been taken, if the errors are obvious, or if they otherwise seriously affect the fairness, integrity or public reputation of judicial proceedings.

Id. (emphasis added). Atkinson, in turn, cited New York Central R.R. Co. v. Johnson, 279 U.S. 310, 49 S.Ct. 300, 73 L.Ed. 706 (1929), and Brasfield v. United States, 272 U.S. 448, 47 S.Ct. 135, 71 L.Ed. 345 (1926). Id. New York Central was a civil jury case in which the Court rejected the contention that counsel’s objection to an allegedly prejudicial summation was not sufficiently specific:

The state, whose interest it is the duty of court and counsel alike to uphold, is concerned that every litigation be fairly and impartially conducted and that verdicts of juries be rendered only on the issues made by the pleadings and the evidence. The public interest requires that the court of its own motion, as is its power and duty, protect suitors in their right to a verdict uninfluenced by the appeals of counsel to passion or prejudice. Where such paramount considerations are involved, the failure of counsel to particularize an exception will not preclude this Court from correcting the error. Brasfield v. United States, 272 U.S. 448, 450, 47 S.Ct. 135, 71 L.Ed. 345.

New York Central, 279 U.S. at 318-19, 49 S.Ct. 300 (additional citations omitted). Brasfield was a criminal jury case in which the Court reversed, in the absence of defense counsel’s objection, because the trial court had asked a deadlocked jury to disclose their numerical division without identifying the side favored by the majority. Brasfield, 272 U.S. at 449-50, 47 S.Ct. 135. Brasfield cited several criminal jury cases, 272 U.S. at 450, 47 S.Ct. 135, of which the earliest is Wiborg v. United States, 163 U.S. 632, 16 S.Ct. 1127, 41 L.Ed. 289 (1896), where the Court reversed for an unpreserved error in the charge, stating: “[I]f a plain error was committed in a matter so absolutely vital to defendants, we feel ourselves at liberty to correct it.” Id. at 658, 16 S.Ct. 1127. In the next decade, the Court reversed a criminal conviction despite lack of precision in an objection to a juror’s qualifications, observing: “In criminal cases courts are not inclined to be as exacting, with reference to the specific character of the objection made, as in civil eases.” Crawford v. United States, 212 U.S. 183, 194, 29 S.Ct. 260, 53 L.Ed. 465 (1909).

The salient characteristic of all these cases is that the issue was whether to correct an unpreserved error that occurred in the conduct of a jury trial. In that context, significant values weigh on both sides of the issue. If the appellate court leaves the error uncorrected, some lawful right of a party will have been denied, and there is a risk that the outcome would have been different had the right been protected. On the other hand, if the appellate court corrects the error, the only available remedy is a remand for a new trial. A legal system seeks to protect rights, but it also takes into account the costs in time, resources, and disruption in the lives of participants, including jurors and witnesses, that result when a case must be tried a second time. To resolve the competing force of these values in the trial context, a reviewing court makes its best estimate of the likelihood that the first jury would have reached a different outcome if the error had not occurred. An estimate is necessary because the first jury is no longer available to advise as to what it would have done in the absence of error, and, even if the jurors could be reassembled, substantial doubt would attend their ability to perform the mentally taxing and inherently speculative task of determining what they would have done had the error not occurred. In recognition of the costs of a second trial to remedy an unpre-served error, a reviewing court uses the power to order one “sparingly,” Jones v. United States, 527 U.S. 373, 389, 119 S.Ct. 2090, 144 L.Ed.2d 370 (1999), and requires one only “in those circumstances in which a miscarriage of justice would otherwise result,” Olano, 507 U.S. at 736, 113 S.Ct. 1770 (internal quotation marks omitted).

By contrast, the context of review of a sentencing error is fundamentally different. From the standpoint of the parties, the error might have great significance. An error yielding an unduly low sentence would deny the public its entitlement to a sentence sufficient to achieve the purposes of punishment. An error yielding an unduly high sentence would deny the defendant freedom for some length of time. More importantly, the cost of correcting a sentencing error is far less than the cost of a retrial. A resentencing is a brief event, normally taking less than a day and requiring the attendance of only the defendant, counsel, and court personnel. Equally important, review of a sentencing error, unlike a trial error, does not require the appellate court to make its estimate of whether it thinks the outcome would have been non-trivially different had the error not occurred. The district court, familiar with that type of task and able to receive submissions of information that is not part of the existing record and that might have been submitted at the time of the original sentence had the Booker standards been in effect, can answer the question whether those standards would have resulted in a non-trivially different sentence at that time. Such an inquiry is very similar to a district court’s task in cases where the outcome of a bench trial is remanded for reconsideration untainted by an error. See Martha Graham School and Dance Foundation, Inc. v. Martha Graham Center of Contemporary Dance, Inc., 380 F.3d 624, 646-47 (2d Cir.2004) (civil bench trial); United States v. Sanders, 205 F.3d 549, 553-54 (2d Cir.2000) (resentencing).

In short, there is no need to apply the plain error doctrine in the sentencing context with precisely the same procedure that has been used in the context of review of errors occurring at trial, whether civil or criminal. Moreover, we note that the Supreme Court has never applied the Ola-no formulation of the plain error doctrine to ignore a judge’s sentencing error that affected substantial rights, nor required a court of appeals to do so.

With these considerations in mind, we examine the three responses that Booker has evoked from courts of appeals when a sentencing judge has committed a Sixth Amendment error, unpreserved for appeal, by finding facts and mandatorily enhancing a sentence above the Guidelines range that would have been applicable solely on the basis of facts found by the jury. The Eleventh Circuit and a panel of the Sixth Circuit have concluded that, except in extraordinary circumstances, the sentence should be affirmed. See Bruce, 396 F.3d at 183; Rodriguez, 398 F.3d at 1301-02, 2005 WL 272952, at *9-*10 (11th Cir. Feb.4, 2005). The Eleventh Circuit has noted that it is difficult to estimate what sentence the sentencing judge would have imposed absent the error, see Rodriguez, 398 F.3d at 1301, 2005 WL 272952, at *9, and the Supreme Court has cautioned that where the effect of error is “so uncertain, a defendant cannot meet his burden of showing that the error actually affected his substantial rights.” Jones, 527 U.S. at 395, 119 S.Ct. 2090. Noting that the Sixth Amendment error is not the use of an enhancement based on facts found by the sentencing judge, a result that1Booker permits, but rather the mandatory use of such an enhancement, the .Eleventh Circuit asks “whether there is a reasonable probability of a different result if the guidelines had been applied in an advisory instead of binding fashion by the sentencing judge in this case.” Rodriguez, 398 F.3d at 1301, 2005 WL 272952, at *9. To this question the Eleventh Circuit responds:

The obvious answer is that we don’t know. If the district court judge in this '.case had the liberty of increasing or decreasing [the defendant’s] sentence . above or below the guidelines range, he might have given [the defendant] a longer sentence, or he might have given a shorter sentence, or he might have given the same sentence. The record provides no reason to believe any result is more likely than the other.. We just don’t know.
Because we don’t know, the Supreme Court’s Jones decision is controlling. It tells us that where the effect of an error on the result in the district court is uncertain or indeterminate — where we would have to speculate — the appellant has not met his burden of showing a reasonable probability that the result would have been different but for the error; he has not met his burden of showing prejudice; he has not met his burden of showing that his substantial rights have been affected. Because this appellant has not carried his burden as to the third prong of the plain error test, we have no occasion to decide how he would have fared under the fourth prong.

Id. at 1301, 2005 WL 272952, at **9-10 (citation omitted).

We agree that the Sixth Amendment error is the mandatory use of the Guidelines enhancement, not the fact of the enhancement. We also agree that as a reviewing court we do not know what the sentence would have been absent the error. We also agree that, absent the error, the sentence might have been different. But we disagree that the consequence of uncertainty must be that the defendant necessarily loses. We disagree because, as we have explained, the trial context differs so fundamentally from the sentencing context as to render inapplicable the precise methodology by which the plain error doctrine has been applied to trial errors. It is simply not so that we “would have to speculate,” id. We can ask the sentencing judge. With that opportunity available, and with no Supreme Court precedent precluding its use, there- is no reason to risk leaving in place a sentence that might be materially lower or higher than the one that would have been imposed without error.

The Third and Fourth Circuits and one panel of the Sixth Circuit have concluded that a Sixth Amendment error in sentencing requires a remand for resentencing. See Davis, 397 F.3d at 183; Oliver, 397 F.3d at 380-81; Hughes, 396 F.3d at 376-77, 384-85. We consider that technique far more consonant with precepts of justice than an affirmance, but it imposes burdens and creates risks that are avoidable. The burdens arise from the need to convene a resentencing hearing, a procedure that sometimes requires brief, testimony and usually requires the presence of the defendant, see Fed.Crim.P. 43(a)(3), who will often be serving a sentence at a distant location. The risks arise from the fact that, if the defendant is resentenced on the basis of circumstances existing at the time of the resentencing, see Werber v. United States, 149 F.3d Í72, 178-79 (2d Cir.1998), new aggravating facts might increase the sentence or new mitigating facts might reduce it. There is no need to accept either these burdens or these risks in cases where the sentencing judge advises that the original sentence would not have been materially different if imposed without error. The automatic remand for resentencing also appears to ignore plain error analysis and results in a remand in some cases where the district judge would not have imposed a materially different sentence in the absence of error. In such cases, the third and fourth Olano factors will not have been satisfied.

To avoid the deficiencies of either a routine affirmance or a routine remand for resentencing, we ruled in Crosby that we would normally remand for determination by the sentencing judge of whether a materially different sentence would have been imposed. This disposition avoids the risk that leniency or harshness resulting from legal error will remain uncorrected, yet it also avoids what might turn out to be the needless burdens and risks of automatic resentencing.

The Eleventh Circuit suggested several deficiencies of the Crosby form of remand, and we take this opportunity to offer a response. First, the Eleventh Circuit viewed a Crosby remand as delegating to the district court the task of making the plain error determination, see Rodriguez, 398 F.3d at 1305, 2005 WL 272952, at *14, contrary to the usual duty of an appellate court to make such determination, see United States v. Dominguez Benitez, 542 U.S. 74, -, 124 S.Ct. 2333, 2340, 159 L.Ed.2d 157 (2004); United States v. Vonn, 535 U.S. 55, 59, 122 S.Ct. 1043, 152 L.Ed.2d 90 (2002). We think that characterization of Crosby is both incomplete and inaccurate. In Crosby, we determined that the first two prongs of Olano were met. There was error, see Booker, — U.S. at --, 125 S.Ct. at 755-56, and it was plain, in the relevant sense that it was “clear,” Olano, 507 U.S. at 734, 113 S.Ct. 1770, under the law applicable “at the time of appellate consideration,” see Johnson v. United States, 520 U.S. 461, 468, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997). As to the third prong, we asked the District Judge to determine whether a materially different sentence would have been imposed absent the error. Admittedly, this assigned the District Judge a role in plain error analysis, but was not an abandonment of the appellate court’s ultimate responsibility. We remanded only after we determined that, on the record in Crosby, we could not say with sufficient confidence that the same sentence would have been imposed. We therefore ruled that, in the sentencing context, the availability of the sentencing judge to advise us made it appropriate to learn authoritatively what would have happened, absent error, rather than make a wrong guess or place on the defendant the risk of serving extra years because he could not prove what the right guess should be. Moreover, our remand demonstrated our decision that the view of the sentencing judge as to whether the sentence would have been materially different would establish to our satisfaction that the third Olano prong was met, or as we put it, would “complete[ ]” the plain error analysis. See Crosby, 397 F.3d at 118. The remand also implicitly indicated our view that the sentencing judge’s conclusion that a materially different sentence would have been imposed would establish to our satisfaction that the fourth Olano prong was met, since leaving in place an error-infected sentence that would have been materially different absent error and that could be readily corrected would “seriously affect[] the fairness, integrity or public reputation of judicial proceedings.” Olano, 507 U.S. at 736, 113 S.Ct. 1770 (internal quotation marks omitted). ■ Indeed, it would seriously affect all three.

The Eleventh Circuit also suggested that Crosby “essentially requires resen-tencing in order to determine whether re-sentencing is required.” Rodriguez, 398 F.3d at 1305, 2005 WL 272952, at. *14. This assertion of tautology reveals a misunderstanding of Crosby. The remand is not to “require! ] resentencing,” as we explicitly explained, Crosby, 397 F.3d at 117-18. The remand is for a determination of whether the original sentence would have been materially different, and only in that event does the remand lead to resentenc-ing.

Finally, the Eleventh Circuit expressed concern that Crosby will lead to too many remands. In our Circuit, when Booker was decided, there were about 200 cases, pending on direct review, in which a pre-Booker sentence might be erroneous under the teachings of Booker. Many of these will likely be remanded pursuant to Crosby. Some of the remands will likely result in resentencing. We do not regard that prospect as an undue burden on the proper functioning of the criminal justice system in the federal courts of this Circuit. On the contrary, we consider it far preferable to leaving some materially erroneous sentences in place simply because we cannot guess what sentencing judges would have done.

In sum, we ' believe that the remand contemplated by Crosby represents a sound application of the plain error doctrine to the context of sentencing, and that the differences between that context and the trial context must not be overlooked. Accordingly, we will remand this case to the District Court for further proceedings in conformity with Booker and Crosby.

Remanded. 
      
      . The airline Williams chose to transport the ammonia was infelicitously (at least on that day) called "Spirit Airlines."
     
      
      . Defense counsel unsuccessfully sought to reduce this four-level enhancement by two levels, a departure authorized by the Guidelines. See U.S.S.G. § 2Q1.2(b)(1)(B), comment. (n.5).
     
      
      . Defense counsel unsuccessfully sought to reduce this nine-level enhancement by three levels, a departure authorized by the Guidelines. See id. § 2Q1.2(b)(2), comment, (n.6).
     
      
      . In Cotton, the error concerned a defect in the indictment, see 535 U.S. at 633-34, 122 S.Ct. 1781; correction of that error would have required a new grand jury proceeding followed by a new trial. In Jones v. United States, 527 U.S. 373, 119 S.Ct. 2090, 144 L.Ed.2d 370 (1999), the error occurred at the sentencing phase of a death penalty case, see id. at 375-79, 119 S.Ct. 2090, and correction of that error would have required a new jury trial for the sentencing phase. See Romano v. Oklahoma, 512 U.S. 1, 13-14, 114 S.Ct. 2004, 129 L.Ed.2d 1 (1994) (alternate holding that even if jury improperly disregarded instructions, gauging effect would involve speculation, not warranting retrial of penalty phase of death penalty case).
     
      
      . In making the estimate necessary to apply the plain error doctrine, the reviewing court does not ask itself whether the outcome would be different at a second trial conducted without the error. It asks whether the outcome of the first trial would have been different without the error. These are not the same questions. The record is available to show what evidence was before the jury at the first trial, thereby providing some basis to assess the likelihood that the absence of error would have yielded a different result. Were the reviewing court to assess the likelihood that a second trial, free of the error, would yield a different result, it would have to undertake the more speculative inquiry as to what evidence would likely be presented at the second trial.
     
      
      . As we have noted, since the enunciation of plain error factors in Olano, the Supreme Court has twice declined to correct an unpre-served sentencing error where correction would have required a retrial by a jury in the penalty phase of a death case. See Jones, 527 U.S. at 375-79, 119 S.Ct. 2090; Romano, 512 U.S. at 13-14, 114 S.Ct. 2004. Nearly 100 years ago, the Court declined to consider a judge's sentencing error in a case from the Supreme Court of the Philippine Islands. Paraiso v. United States, 207 U.S. 368, 28 S.Ct. 127, 52 L.Ed. 249 (1907). It appears that the sentencing claim was not assigned as error to the United States Supreme Court, and, in any event, the writ of error was dismissed for want of jurisdiction. Id. at 370, 28 S.Ct. 127. Three years later, the Court entertained and sustained an unpreserved claim that a sentence violated the Eighth Amendment. Weems v. United States, 217 U.S. 349, 362, 30 S.Ct. 544, 54 L.Ed. 793 (1910). The significance of Paraíso was undermined by the Court’s observation that in that case "[i]t may be that we were not sufficiently impressed with the importance of [the sentencing] contentions." Id. at 362, 30 S.Ct. 544. In Bartone v. United States, 375 U.S. 52, 84 S.Ct. 21, 11 L.Ed.2d 11 (1963), the Court corrected as "plain” a sentencing judge's error in adding one day to a one-year sentence in the absence of the defendant.
      Appeals in federal sentencing cases did not occur frequently until 1987 when the Sentencing Reform Act of 1984 became effective.
     
      
      . In this Circuit, when the error results from an intervening change in the law, we have applied a modified version of the plain error doctrine whereby the burden is on the Government to show that the error did not affect substantial rights. See United States v. Viola, 35 F.3d 37, 42 (2d Cir.1994) (abrogated on other grounds, Salinas v. United States, 522 U.S. 52, 118 S.Ct. 469, 139 L.Ed.2d 352 (1997)). We have recognized, but not resolved, the issue of whether this modified plain error doctrine has been implicitly rejected by Johnson v. United States, 520 U.S. 461, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997). See United States v. Thomas, 274 F.3d 655, 668 n. 15 (2d Cir.2001) (in banc). For purposes of the pending appeal, we will assume that the burden to show that an error, arising from an intervening change in law, affected substantial rights remains with the defendant.
     
      
      . An appellate court, confined to the record of the prior sentencing, would often have difficulty if it tried to estimate whether the district court, absent a sentencing error, would have imposed a materially different sentence. The question can be better answered on a remand, at which the district court would be able to receive and evaluate submissions from the parties of circumstances, existing at the time of the original sentencing, that .might have materially altered the original sentence had the Guidelines been only advisory.
     
      
      . For the view that uncertainty as to outcome leaves a defendant without a remedy, the ' Eleventh Circuit drew support from the Supreme Court’s decision in United States v. Dominguez Benitez, 542 U.S. 74, -, 124 S.Ct. 2333, 2340, 159 L.Ed.2d 157 (2004). See Rodriguez, 398 F.3d at 1302, 2005 WL 272952, at *11. That decision, applying plain error analysis in the context of an error in accepting a guilty plea, ruled that a defendant must show a reasonable probability that, but for the error, he would not. have entered the guilty plea. See Dominguez Benitez, 542 U.S. at -, 124 S.Ct. at 2336. Obviously, courts cannot rely conclusively on a defendant who wants to withdraw a guilty plea for the estimate of what the defendant would have done in the absence of error in accepting the plea. On a clear record, the appellate court will make the estimate, as the Supreme Court did in Dominguez Benitez, but, interestingly, it is not uncommon, where the record is uncertain, for appellate courts to remand so that the estimate can be made by the district court, with the traditionally more comprehensive view of the circumstances that prevailed when the plea was entered. See United States v. Colon-Torres, 382 F.3d 76, 91 (1st Cir.2004); United States v. Graves, 374 F.3d 80, 85 (2d Cir.2004).
      
        United States v. Vonn, 535 U.S. 55, 59, 122 S.Ct. 1043, 152 L.Ed.2d 90 (2002), additionally relied on by the Eleventh Circuit, also involved the application of plain error analysis to an error in accepting a guilty plea.
     
      
      . In unpublished opinions (unavailable for citation to the Ninth Circuit or by courts of that Circuit, see 9th Cir. R. 36-3), panels of the Ninth Circuit have also vacated sentences that violate the Sixth Amendment under Booker and remanded for resentencing. See United States v. Reynolds, 121 Fed.Appx. 247 (9th Cir. Feb.7, 2005); United States v. Stewart, 121 Fed.Appx. 713, 2005 WL 281418 (9th Cir. Feb.7, 2005); United States v. McCoun, 121 Fed.Appx. 246 (9th Cir. Feb.7, 2005). In a variation that approaches a Crosby remand, another Ninth Circuit panel vacated a sentence and remanded “so that the district judge may determine whether the change in the law would make a difference in the sentencing of this case. If the district judge determines that it does, he may vacate the sentence and resentence [the defendant].” United States v. Seibert, 121 Fed.Appx. 715, 2005 WL 281469 (9th Cir. Feb.7, 2005). This form of remand is not a Crosby remand, which instructs the district judge to determine whether the change in the law would have made a material difference in the original sentence. Seibert appears to ask the district judge whether the change would make a difference at a resentencing.
     
      
      . The Fourth Circuit used a remand for required resentencing in Hughes as to a sentence that had been imposed before that Circuit instructed sentencing judges, in the aftermath of Blakely but before Booker, to apply the Guidelines and also state an alternative sentence that would be imposed if the Guidelines were advisory. See United States v. Hammoud, 381 F.3d 316, 353-54 (4th Cir.2004), judgment vacated, - U.S. -, 125 S.Ct. 1051, 160 L.Ed.2d 997 (2005). We do not yet know what disposition the Fourth Circuit will make as to cases involving alternátive sentences stated, but not formally imposed, pursuant to Hammoud.
      
     
      
      . The Sixth Circuit has suggested that a district judge's mandatory use of the Guidelines to find facts that enhance a sentence satisfies the third and fourth Olano factors because "[i]t is clear that had the district court not found facts on its own at sentencing, which under Booker constitutes a violation of the Sixth Amendment, [the defendant’s] sentence would have been materially different.” United States v. Milan, 398 F.3d 445, 452, 2005 WL 309934, at *5 (6th Cir. Feb. 10, 2005). However, the more important point is that had the district judge committed no error at all, i.e., sentenced as Booker now instructs, he might have imposed precisely the same sentence. For an error to affect substantial rights, it "must have affected the outcome,” Olano, 507 U.S. at 734, 113 S.Ct. 1770, which, in the sentencing context, must mean an outcome non-trivially different from the outcome that would have occurred in tire absence of the error.
     
      
      . The Sixth Circuit has also described Crosby, inaccurately in our view, as requiring the district court "itself [to] conduct a plain or harmless error inquiry in order to determine whether it ought to resentence the defendant.” Milan, 398 F.3d at 453, 2005 WL 309934, at *6.
     
      
      . It might be argued that, in the sentencing context, where error can be easily corrected, the requirement that an error be "plain” is ill-advised. Although there is a sound reason not to require a new trial because of an un-preserved error that is not "plain,” a sentence ought not to impose too few or too many years just because the error took some thought for the appellate court to identify. However, Rule 52(b) establishes the requirement that the error be "plain,” and we have no occasion on this appeal, nor did we in Crosby, to consider whether the second Olano prong should be ameliorated in the context of sentencing errors.
     
      
      . We could have required the case to be restored to our jurisdiction immediately after the district judge decided whether the original sentence would have been materially different, and then affirmed whenever the district judge’s answer was "no” or remanded for resentencing whenever the district judge’s answer was "yes.” That procedure would have precipitated needless yo-yoing between the appellate court and the district court simply to enable the appellate court to announce the outcome of applying the third and fourth Ola-no factors in each case. It was more efficient to announce ahead of time that if the district judge’s answer was "yes,” that decision would, in our assessment, satisfy the third and fourth Olano factors.
     
      
      . Because the sentence in the pending appeal was imposed prior to Booker, we intimate no views as to the proper application of plain error analysis to sentences imposed after Booker.
      
     