The government’s obligations under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), are seemingly well-established. The prosecution has a constitutional duty to disclose evidence favorable to an accused when such evidence is material to guilt or punishment. See Brady, 373 U.S. at 87, 83 S.Ct. 1194. This duty covers not only exculpatory material, but also information that could be used to impeach a key government witness. See Giglio v. United States, 405 U.S. 150, 154, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972). Brady does not, however, require the prosecution to disclose all exculpatory and impeachment material; it need disclose only material “that, if suppressed, would deprive the defendant of a fair trial.” United States v. Bagley, 473 U.S. 667, 675, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985). In the context of Brady, a defendant is deprived of a fair trial only where there is a reasonable probability that the government’s suppression affected the outcome of the case, see id. at 682, 105 S.Ct. 3375, or where the suppressed evidence “could reasonably be taken to put the whole ease in such a different light as to undermine confidence in the verdict,” Kyles v. Whitley, 514 U.S. 419, 435, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995).
With respect to when the prosecution must make a disclosure required by Brady, the law also appears to be settled. Brady material must be disclosed in time for its effective use at trial, see, e.g., Leka v. Portuondo, 257 F.3d 89, 100 (2d Cir.2001), or at a plea proceeding, see United States v. Persico, 164 F.3d 796, 804 (2d Cir.1999); Tate v. Wood, 963 F.2d 20, 24 (2d Cir.1992). The United States District Court for the Eastern District of New York (I. Leo Glasser, Judge), however— reinterpreting Brady and its progeny— held that, in all cases, the Constitution requires the government to provide a defendant with all exculpatory and impeachment materials immediately upon request by a defendant, even if the request is made far in advance of trial. See United States v. Shvarts, 90 F.Supp.2d 219, 224-29 (E.D.N.Y.2000); Trial Transcript at 58, 69-70 (Feb. 2, 2001) (applying Shvarts to the case at hand). The District Court carved out a limited exception to its holding for evidence that, if disclosed, could endanger a potential government witness; however, it ruled that, in all other instances, the prosecution has a constitutional duty to disclose all Brady and Giglio material immediately upon request by the defense. In response to this ruling, the Government filed a petition for a writ of mandamus.
I., Background
This petition arises out of a February 2, 2001, scheduling order issued by the District Court in preparation for trial.
Defendants stand accused in an indictment returned on March 1, 2000, with engaging in various crimes related to a large-scale stock fraud and money-laundering scheme.1 Before a trial date had been set,2 several of the defendants moved between November 2000 and February 2001 to compel the Government to disclose immediately all exculpatory and impeachment material in its possession. The District Court held a hearing on February 2, 2001, and granted defendants’ motions. The District Court based its decision on its prior ruling in United States v. Shvarts, 90 *136F.Supp.2d 219 (E.D.N.Y.2000), where it had held that the Due Process Clause of the Fifth Amendment requires the prosecution to disclose all exculpatory and impeachment materials as soon after an indictment as such materials are requested by a defendant. See 90 F.Supp.2d at 224-29.
After the indictment had been filed in Shvarts, the defendants had requested the prosecution to provide, far in advance of trial, all exculpatory and impeachment evidence that was in its possession. The prosecutor in Shvarts had agreed to disclose immediately to the defendants all exculpatory information encompassed by Brady, but had refused to release impeachment evidence relating to potential government witnesses until, in his view, such evidence was needed by the defendants for use at trial. See id. at 225. The prosecutor had argued that Brady and Giglio did not require him to disclose all Brady and Giglio materials immediately upon request by a defendant; in his view, those cases merely required him to disclose such materials in time for the defendant to use them effectively at trial.
The District Court rejected this argument. It noted that, in Brady, the Supreme Court held that a defendant’s constitutional rights are violated if the prosecution fails to produce exculpatory evidence “on demand of an accused.” See Shvarts, 90 F.Supp.2d at 226 (quoting Brady, 373 U.S. at 87-88, 83 S.Ct. 1194). The District Court reasoned that the Supreme Court’s use of the words “on demand of an accused,” indicates that the prosecution has an obligation to turn over all exculpatory material — in-eluding impeachment evidence relating to potential government witnesses — -as soon as a defendant requests such material. See id. at 226. Moreover, according to the District Court, the “materiality” of the exculpatory or impeachment material — that is, whether its suppression would deprive defendants of a fair trial — need not be considered when defining the scope of a defendant’s constitutional right to disclosure.3 See id. The District Court therefore ordered the prosecutor in Shvarts to disclose immediately to the defendants all impeachment material in its possession. The District Court held, however, that if the prosecutor believed that “immediate disclosure of impeachment evidence would pose a serious threat to the life or safety of a prospective witness,” he could file an ex parte application to modify the scope of the order. See id. at 229. The prosecutor in Shvarts, for reasons that are not disclosed in the record of the instant case, did not seek appellate review of the District Court’s order.
The Government was soon presented, however, with another opportunity to challenge the rule enunciated by Judge Glas-ser in Shvarts. Like the defendants in Shvarts, defendants here moved far in advance of trial, pursuant to Brady and Gig-lio, to compel the Government to disclose immediately all exculpatory material and impeachment material relating to potential government witnesses. As in Shvarts, the Government agreed to disclose immediately all exculpatory information encompassed by Brady, but refused to turn over impeachment evidence relating to potential government witnesses. The Government argued that immediate disclosure of im-*137peaehment evidence was not compelled by Brady or Giglio, and contended that impeachment material could be released much closer to the time of trial. The District Court disagreed. It adhered to the approach that it had adopted in Shvarts and granted defendants’ motions. The District Court therefore ordered the immediate disclosure of all impeachment materials in possession of the Government, unless the Government could show that such disclosure would endanger the life or safety of a potential witness. When the Government suggested that it might seek review of the District Court’s decision, the District Court acknowledged the Government’s “very strong interest in having the Shvarts case tested” and indicated that it would welcome appellate consideration of the issue. The Government subsequently filed the instant petition seeking an order compelling the District Court to vacate that portion of its February 2, 2001, scheduling order requiring the Government (in accordance with the general rule of constitutional law enunciated in Shvarts) to immediately produce all impeachment material.
In support of its petition, the Government argues that the District Court exceeded its authority in finding that it had a constitutional obligation to immediately disclose impeachment material relating to potential government witnesses upon defendants’ request. According to the Government, such disclosure is not required by Brady or Giglio and, moreover, is prohibited by a key provision of the Jencks Act, 18 U.S.C. § 3500, which provides in substance that no statement made by a government witness or prospective government "witness shall be the subject of discovery until that witness has testified on direct examination.4 See Fed.R.Crim.P. 26.2 (2001) (incorporating the Jencks Act).5
Defendants argue that the District Court acted within its discretionary authority in fashioning “what amounts to an individual procedural order” which it applied in managing pretrial discovery, and, therefore, mandamus is inappropriate.
II. Availability of Mandamus Review
Pretrial discovery orders, such as the one here, are generally not reviewable by means of direct appeal, and “we have expressed reluctance to circumvent this salutary rule by use of mandamus.” In re W.R. Grace & Co., 984 F.2d 587, 589 (2d Cir.1993) (citations omitted); see, e.g., In re Weisman, 835 F.2d 23, 25 (2d Cir.1987); In re United States, 680 F.2d 9, 12 (2d Cir.1982). Nevertheless, we will entertain a petition for a writ of mandamus-which, as we have often noted, is an extraordinary remedy-to cure a defective pretrial discovery order if the petitioner demonstrates “(1) the presence of a novel *138and significant question of law; (2) the inadequacy of other available remedies; and (3) the presence of a legal issue whose resolution will aid in the administration of justice.” In re United States, 903 F.2d 88, 89 (2d Cir.1990); see Chase Manhattan Bank, N.A. v. Turner & Newall, PLC, 964 F.2d 159 (2d Cir.1992) (using these criteria to determine the availability of the writ of mandamus to remedy a discovery order); In re von Bulow, 828 F.2d 94, 97-100 (2d Cir.1987) (same). See generally American Express Warehousing, Ltd. v. Transamerica Ins. Co., 380 F.2d 277, 282 (2d Cir.1967) (“When a discovery question is of extraordinary significance or there is extreme need for reversal of the district court’s mandate before the case goes to judgment, there are escape hatches from the finality rule.... ”). We believe that the Government, as petitioner, has satisfied all three of these “stringent” requirements here. In re United States, 10 F.3d 931, 933 (2d Cir.1993).
First, as the District Court itself recognized, see Hearing Transcript at 60 (Feb. 2, 2001), this appeal presents “a novel and significant question of law,” In re United States, 903 F.2d at 89. Our research has unearthed no case from a Court of Appeals that has adopted the District Court’s rule that, in all cases, a prosecutor is constitutionally required to provide exculpatory and impeachment material immediately upon demand of a defendant, even if made far in advance of trial, without regard to its “materiality.” Moreover, only a few district judges have adopted this rule, and some have explicitly rejected it. Compare, e.g., United States v. Snell, 899 F.Supp. 17, 20-21 (D.Mass.1995) (Nancy Gertner, J.) (adopting a position similar to that of Judge Glasser), and United States v. Owens, 933 F.Supp. 76 (D.Mass.1996) (William G. Young, J.) (same), with, e.g., United States v. Jacques Dessange, Inc., No. 99 CR. 1182, 2000 WL 280050, at*7-*9 (S.D.N.Y. Mar. 14, 2000) (Denise Cote, J.) (discussing and rejecting Judge Glasser’s position), and United States v. Jones, No. 00 CR. 182, 2000 WL 1448640, at *l-*2 (S.D.N.Y. Sept.28, 2000) (John G. Koeltl, J.) (similar). There is also no doubt that the timing of disclosure under Brady and Giglio may be of critical importance in many criminal cases.
Second, the petitioner has no other means of protecting its interests. Pretrial discovery orders in civil or criminal cases are generally not directly appealable prior to the entry of judgment. See Church of Scientology v. United States, 506 U.S. 9, 18 n. 11, 113 S.Ct. 447, 121 L.Ed.2d 313 (1992); Chase Manhattan Bank, 964 F.2d at 162-63; see also United States v. Vargas, 596 F.2d 1, 2 (1st Cir.1979) (per cu-riam) (“Civil and criminal pretrial discovery orders are subject to the same rule precluding appeal before final judgment.”). Without mandamus, therefore, the Government would either have to comply with the District Court’s scheduling order, or risk contempt for failure to comply, exclusion of its witnesses, or dismissal of the indictment. Compliance with the scheduling order would require the Government to identify many of its potential witnesses to the defense far in advance of trial, thereby creating the very risks that the Jencks Act and Rule 26.2 were designed to avoid, such as increasing the chances that witnesses will be threatened or intimidated. See, e.g., United States v. Presser, 844 F.2d 1275, 1285 (6th Cir.1988) (discussing the importance of protecting potential government witnesses from threats of harm and other intimidation before they testify at trial). The District Court was mindful of this concern in permitting the Government to file an ex parte application to delay discovery where “immediate disclosure of impeachment evidence would pose a serious threat to the life or safety of a pro*139spective witness,” Shvarts, 90 F.Supp.2d at 229; however, this remedy does not address the Government’s justifiable concerns regarding the risk of witness tampering in circumstances where there is no evidence that the life or safety of a prospective witness is in danger. Moreover, early disclosure of the identities of potential witnesses could undermine undercover operations and ongoing investigations involving these witnesses. Accordingly, if the Government’s claims are meritorious, mandamus is the only adequate remedy available here.
Third and finally, resolution of the issue presented here will aid in the administration of justice. There is currently a significant divergence of views among district judges of this Circuit concerning the correctness of the District Court’s ruling. Compare Shvarts, 90 F.Supp.2d at 226 (I. Leo Glasser, J.) (requiring the Government to produce Giglio material before trial), and United States v. Lino, No. 00 CR. 632, 2001 WL 8356, at *14-*17 (S.D.N.Y. Dec.29, 2000) (William H. Pauley III, J.) (requiring the Government to produce certain Giglio material before trial because of the importance to the Government’s case of a particular witness), with United States v. Pimentel, No. 99 CR 1104, 2001 WL 185053, at *5-*6 (E.D.N.Y. Jan 22., 2001) (Sterling Johnson, Jr., J.) (holding that there is no obligation to produce Giglio material before trial), United States v. Jacques Dessange, Inc., No. 99 CR. 1182, 2000 WL 280050, at*7-*9 (S.D.N.Y. Mar. 14, 2000) (Denise Cote, J.) (same), and United States v. Avellino, 129 F.Supp.2d 214, 217-18 (E.D.N.Y.2001) (Denis R. Hurley, J.) (holding that the timetable for disclosure under Brady and Giglio depend on the nature of the evidence involved). See generally Robert G. Morvillo & Robert J. Anello, White Collar Crime: Disclosure of ‘Giglio’ Material, N.Y. L.J., June 5, 2001, at 3 (discussing conflicting decisions). Resolution of the issue before us will reduce the uncertainty reflected in these opinions and “add importantly to the efficient administration of justice.” In re von Bulow, 828 F.2d at 99 (quoting Colonial Times, Inc. v. Gasch, 509 F.2d 517, 524 (D.C.Cir.1975)).
Having determined that the issues raised here warrant consideration on a petition for extraordinary relief, we now turn to the merits of that petition.
III. MERITS OF THE PETITION
The basic rule of Brady is that the Government has a constitutional duty to disclose favorable evidence to the accused where such evidence is “material” either to guilt or to punishment. See Brady, 373 U.S. at 87, 83 S.Ct. 1194. Favorable evidence includes not only evidence that tends to exculpate the accused, but also evidence that is useful to impeach the credibility of a government witness. See Giglio, 405 U.S. at 154, 92 S.Ct. 763.
Because Brady and its progeny are grounded in the Due Process Clauses of the Constitution, the essential purpose of the rules enunciated in these cases is to protect a defendant’s right to a fair trial by ensuring the reliability of any criminal verdict against him. See Bagley, 473 U.S. at 675, 105 S.Ct. 3375. Thus, a Brady violation occurs only where the government suppresses evidence that “could reasonably [have been] taken to put the whole case in such a different light as to undermine confidence in the verdict.” Kyles v. Whitley, 514 U.S. 419, 435, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995); accord Bagley, 473 U.S. at 678, 105 S.Ct. 3375; see also United States v. Agurs, 427 U.S. 97, 112, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976) (holding that Brady’s materiality standard “reflect[s] our overriding concern with the justice of the finding of guilt”).
*140A. Three Components of a Brady Violation
Although the government's obligations under Brady may be thought of as a constitutional duty arising before or during the trial of a defendant, the scope of the government's constitutional duty-and, concomitantly, the scope of a defendant's constitutional right-is ultimately defined retrospectively, by reference to the likely effect that the suppression of particular evidence had on the outcome of the trial. See Strickler v. Greene, 527 U.S. 263, 281, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999) ("[S]trictly speaking, there is never a real `Brady violation' unless the [Government's] nondisclosure was so serious that there is a reasonable probability that the suppressed evidence would have produced a different verdict."); see also Bagley, 473 U.S. at 699, 105 S.Ct. 3375 (Marshall, J., dissenting) ("[Brady] defines [a defendant's] right not by reference to the possible usefulness of the particular evidence in preparing and presenting the case, but retrospectively, by reference to the likely effect the evidence will have on the outcome of the trial."). The government therefore has a so-called "Brady obligation" only where non-disclosure of a particular piece of evidence would deprive a defendant of a fair trial. See Bagley, 473 U.S. at 675, 105 S.Ct. 3375; Agurs, 427 U.S. at 108, 96 S.Ct. 2392. To demonstrate such a deprivation, a defendant must show that: (1) the Government, either willfully or inadvertently, suppressed evidence; (2) the evidence at issue is favorable to the defendant; and (3) the failure to disclose this evidence resulted in prejudice. See Strickler, 527 U.S. at 281-82, 119 S.Ct. 1936.
In the thirty-eight years since Brady was decided, the Supreme Court has issued a series of rulings that have clarified the scope of these three components of a Brady violation. Most of these rulings have focused on the second and third corn-ponents-which, together, define what evidence must be disclosed. See, e.g., Bagley, 473 U.S. at 678, 105 S.Ct. 3375 (defining "material" exculpatory evidence as evidence that, if suppressed, would "undermine the confidence in the outcome of a trial"); Giglio, 405 U.S. at 151, 92 S.Ct. 763 (1972) (holding that exculpatory evidence under Brady includes evidence that could be used to impeach a key government witness). Some of the Court's rulings have also addressed the first component of a Brady violation-that is, what it means ror the Government to "suppress" evidence. For example, a prosecutor can be held to have suppressed evidence within the meaning of Brady even if the defendant has not requested such evidence, see Bagley, 473 U.S. at 682, 105 S.Ct. 3375; Agurs, 427 U.S. at 107-11, 96 S.Ct. 2392; and a prosecutor can "suppress" evidence even if he has acted in good faith and even if the evidence is "known only to police investigators and not to the prosecutor," Kyles, 514 U.S. at 438, 115 S.Ct. 1555 (explaining that the Government should actively seek Brady material in its files and in the files of related agencies reasonably expected to have possession of such information).
The central issue here is whether, as a general rule, due process of law requires that the Government, following indictment, disclose all exculpatory and impeachment material immediately upon demand by a defendant. The District Court held that it does. We conclude, however, that the District Court erred with respect to both the scope and the timing of the disclosure required by the Constitution.
B. The Scope and Timing of the Required Disclosure
The scope of the disclosure required by Brady, as enunciated by the Supreme *141Court, has evolved over time. In Brady itself, the Court stated:
We now hold that the suppression by the prosecution of evidence favorable to the accused upon request violates due process where the evidence is material either to guilt or to punishment ...
373 U.S. at 87, 83 S.Ct. 1194 (emphasis added). In this sentence, the Court appears to be using the word “material” in its evidentiary sense, ie., evidence that has some probative tendency to preclude a finding of guilt or lessen punishment, cf. Fed.R.Evid. 401.6
Thirteen years later, however, in United States v. Agurs, 427 U.S. 97, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976), the Court began a process that would result in the word “material” in the Brady context having an entirely different meaning. The Court said:
[UJnless the omission deprived the defendant of a fair trial, there was no constitutional violation requiring the verdict to be set aside; and absent a constitutional violation, there was no breach of the prosecutor’s constitutional duty to disclose.
But to reiterate a critical point, the prosecutor imll not have violated his constitutional duty of disclosure unless the omission is of sufficient significance to result in the denial of a defendant’s right to a fair trial.
427 U.S. at 108, 96 S.Ct. 2392 (emphasis added). The Court quoted these words in full nine years later in United States v. Bagley, 473 U.S. 667, 675-76, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985).
Bagley made explicit what Agurs foreshadowed: that “material” in the Brady context does not mean material in the evidentiary sense, as Brady seemed to suggest. Rather, evidence is material in the Brady context only if “its suppression undermines confidence in the outcome of the trial.” Id. at 678, 105 S.Ct. 3375; see also Pennsylvania v. Ritchie, 480 U.S. 39, 57, 107 S.Ct. 989, 94 L.Ed.2d 40 (1987) (using the Bagley standard of materiality to define the scope of a Brady disclosure obligation). The Court went on to give some content to the “undermines confidence in the outcome” standard, stating that, for Brady purposes,
evidence is material only if there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different. A “reasonable probability” is a probability sufficient to undermine confidence in the outcome.
Id. at 682, 105 S.Ct. 3375.
More recently, in Kyles v. Whitley, 514 U.S. 419, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995), the Court explicitly stated that what it called “the current Brady law,” 514 U.S. at 433, 115 S.Ct. 1555, imposes a disclosure obligation narrower in scope than the obligation to disclose all evidence favorable to the defendant:
[T]he rule in Bagley (and, hence, in Brady) requires less of the prosecution than the ABA Standards for Criminal Justice, which call generally for prosecu-torial disclosures of any evidence tending to exculpate or mitigate.
Id. at 437, 115 S.Ct. 1555 (citing ABA Standards for Criminal Justice, Prosecution Function and Defense Function 3-*1423.11(a) (3d ed.1993); ABA Model Rule of Professional Conduct 3.8(d) (1984)).7
The result of the progression from Brady to Agurs and Bagley is that the nature of the prosecutor’s constitutional duty to disclose has shifted from (a) an evidentiary test of materiality that can be applied rather easily to any item of evidence (would this evidence have some tendency to undermine proof of guilt?) to (b) a result-affecting test that obliges a prosecutor to make a prediction as to whether a reasonable probability will exist that the outcome would have been different if disclosure had been made. To put it another way, Bagley makes the extent of the disclosure required by Brady dependent on the anticipated remedy for violation of the obligation to disclose: the prosecutor must disclose evidence if, without such disclosure, a reasonable probability will exist that the outcome of a trial in which the evidence had been disclosed would have been different. Although many cases continue to use the phrase “Brady material” to mean all exculpatory evidence and the phrase “Giglio material” to mean all impeachment evidence, these characterizations no longer have such broad meaning after Agurs and Bagley.
Like the extent of the required disclosure, the timing of a disclosure required by Brady is also dependent upon the anticipated remedy for a violation of the obligation to disclose: the prosecutor must disclose “material” (in the Agurs! Bagley sense) exculpatory and impeachment information no later than the point at which a reasonable probability will exist that the outcome would have been different if an earlier disclosure had been made. Cf. Leka v. Portuondo, 257 F.3d 89, 100 (2d Cir.2001) (“It is not feasible or desirable to specify the extent or timing of [the] disclosure Brady and its progeny require, except in terms of the sufficiency, under the circumstances, of the defense’s opportunity to use the evidence when disclosure is made.” (emphasis added)). Thus, we have never interpreted due process of law as requiring more than that Brady material must be disclosed in time for its effective use at trial, see id.; see also United States v. Smith Grading & Paving, Inc., 760 F.2d 527, 532 (4th Cir.1985) (same); United States v. Starusko, 729 F.2d 256, 262 (3d Cir.1984) (same); United States v. Olson, 697 F.2d 273, 275 (8th Cir.1983) (same); United States v. Attain, 671 F.2d 248, 255 (7th Cir.1982) (same); United States v. Pollack, 534 F.2d 964, 973 (D.C.Cir.1976) (same); cf. United States v. O’Keefe, 128 F.3d 885, 898 (5th Cir.1997) (similar), or at a plea proceeding, see United States v. Persico, 164 F.3d 796, 804 (2d Cir.1999); Tate v. Wood, 963 F.2d 20, 24 (2d Cir.1992); Miller v. Angliker, 848 F.2d 1312, 1322 (2d Cir.1988); see also Sanchez v. United States, 50 F.3d 1448, 1453 (9th Cir.1995).8 But see Matthew v. Johnson, 201 F.3d 353, 360-62 (5th Cir.2000) (suggesting that Brady may not apply if a defendant’s conviction is based on a guilty plea).
*143The linking of the scope of the disclosure obligation with the remedy for its breach creates both a responsibility and a problem for the prosecutor. An assessment of whether an outcome would have been different if undisclosed evidence had been disclosed is best made after a trial is concluded. At that point the significance of the undisclosed evidence can be considered in light of the strength of all the evidence indicating guilt. The prosecutor, however, cannot await the outcome and must therefore make a prediction before the trial as to how the nondisclosure of favorable evidence will be viewed after the trial. The Supreme Court explicitly recognized this difficulty in Kyles:
[T]he prosecution, which alone can know what is undisclosed, must be assigned the consequent responsibility to gauge the likely net effect of all such evidence and make disclosure when the point of ‘reasonable probability’ is reached.
Kyles, 514 U.S. at 437, 115 S.Ct. 1555 (quoting United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985)).
In some circumstances, the prosecutor’s prediction of “reasonable probability” will be easily made. For example, if there are three eyewitnesses who have told investigators that the perpetrator is someone other than the defendant, there will almost always be a reasonable probability that the disclosure of such evidence would have resulted in a different outcome from a trial at w^hich it was not disclosed, regardless of the strength of the prosecution’s evidence. At the other extreme, an item of evidence with some arguably exonerating effect might be so trivial in significance to the entire trial evidence that there is no reasonable probability that its disclosure would have altered the outcome. But much evidence favorable to a defendant will lie between these extremes, obliging prosecutors to make a careful prediction as to when the “point of ‘reasonable probability’ is reached.” Id. Of course, as the Supreme Court has pointed out, a prosecutor “anxious about tacking too close to the wind will disclose a favorable piece of evidence.” Id. at 439, 115 S.Ct. 1555.
Prosecutors with a clear understanding of Brady / Giglio requirements and of their professional responsibilities will readily be able to observe the applicable standards. In rare cases of a constitutional violation, judicial relief can be expected.
In this case, the parties agree that the District Court used the terms “Brady material” and “Giglio material” to mean all exculpatory and impeachment evidence, and that the District Court’s order of February 2, 2001, requires the Government to disclose all impeachment evidence in its possession without regard to its “materiality” in the Agurs/Bagley sense, cf. Shvarts, 90 F.Supp.2d at 226 (“It is sufficient to acknowledge ... the constitutional obligation [to disclose], without the necessity to discuss the requirement of ‘materiality’ as a precondition to its violation.” (emphasis added)), and without regard to whether the Government’s voluntary disclosure was being made so late as to create a reasonable probability of a different result at trial or at a plea proceeding if an earlier disclosure had been made. The District Court believed that it was compelled to issue the order by “the explicit declaration in Brady that ‘[a] prosecution that withholds evidence on demand of an accused which, if made available, would tend to exculpate him or reduce the penalty, helps shape a trial that bears heavily on the defendant,”’ as well as the Supreme *144Court’s repetition in Weatherford v. Bursey, 429 U.S. 545, 559, 97 S.Ct. 837, 51 L.Ed.2d 30 (1977) of the statement of the United States Court of Appeals for the Fourth Circuit that, pursuant to Brady,
[t]he prosecution has the “duty under the due process clause to ensure that ‘criminal trials are fair’ by disclosing evidence favorable to the defendant wpon request.”
Shvarts, 90 F.Supp.2d at 226 (emphasis in original, citations omitted). We disagree.
Neither the Supreme Court nor any Court of Appeals has given the words in Brady, “on demand of an accused,” the temporal significance attributed to these words by the District Court. The reference to “on demand of an accused” merely indicates that, in evaluating a claim that a prosecutor had suppressed exculpatory evidence, the Supreme Court once placed some significance on whether the defendant had made a request for such evidence. Specifically, in evaluating such a claim, the Supreme Court distinguished among three situations: (1) where a defendant made a specific request for the exculpatory evidence at issue; (2) where a defendant made only a general request for exculpatory evidence; and (3) where a defendant made no request at all. See Agurs, 427 U.S. at 103-08, 96 S.Ct. 2392. Thirteen years after its path-breaking opinion in Brady, the Supreme Court in Agurs suggested that the proper standard for evaluating a Brady claim might depend on which of these three situations was present. See Agurs, 427 U.S. at 103-08, 96 S.Ct. 2392. But nine years after Agurs, the Court in Baglay disavowed any difference among the three situations and held that, regardless of a defendant’s request, the government violates its duties under Brady if it suppresses evidence that, if disclosed, would have had a reasonable probability of changing the outcome of the proceedings. See Baglay, 473 U.S. at 681-82, 105 S.Ct. 3375.
It thus appears that Brady’s reference to “on demand of an accused” signified the importance that the Supreme Court placed in the 1960s and 1970s on whether a defendant actually requested exculpatory material. In nearly four decades of jurisprudence, the Supreme Court has never suggested that the reference reflected a constitutional duty to disclose Brady and Giglio materials as soon after indictment as such materials are requested. Indeed, a rule that makes the timing of disclosure dependent on the defendant’s demand is directly contrary to the principle that a prosecutor’s Brady obligation is independent of a defendant’s request for Brady materials. See Bagley, 473 U.S. at 682-83, 105 S.Ct. 3375 (explaining that a defendant’s failure to request Brady material does not free a prosecutor of its obligation to disclose such material).
Accordingly, we reiterate the longstanding constitutional principle that as long as a defendant possesses Brady evidence in time for its effective use, the government has not deprived the defendant of due process of law simply because it did not produce the evidence sooner. There is no Brady violation unless there is a reasonable probability that earlier disclosure of the evidence would have produced a different result at trial, see, e.g., United States v. Romero, 54 F.3d 56, 61 (2d Cir.1995); United States v. Bejasa, 904 F.2d 137, 140 (2d Cir.1990), or at a plea proceeding, see Persico, 164 F.3d at 804.9
*145C. Brady and the Jencks Act
If the Government were seeking mandamus review of a purely discretionary discovery order, we might be reluctant to grant the writ in this case, as “[c]ourts faced with petitions for the peremptory writs must be careful lest they suffer themselves to be misled ... into interlocutory review of nonappealable orders on the mere ground that they may be erroneous.” Will v. United States, 389 U.S. 90, 99 n. 6, 104, 88 S.Ct. 269, 19 L.Ed.2d 305 (1967); see also In re Weisman, 835 F.2d 23, 27 (2d Cir.1987); United States v. DiStefano, 464 F.2d 845, 850 (2d Cir.1972) (holding that a claim that “the judge was wrong, indeed very wrong ... is not enough” to invoke mandamus). Because the District Court’s order in this case included all impeachment materials, however, it implicated the Jencks Act, 18 U.S.C. § 3500,10 which provides that no prior statement made by a government witness shall be the subject of discovery until that witness has testified on direct examination.11 We have previously held that Jencks Act prohibits a District Court from ordering the pretrial disclosure of witness statements. See In re United States, 834 F.2d 283, 286-87 (2d Cir.1987) (granting mandamus to vacate order requiring production of witness statements); United States v. Percevault, 490 F.2d 126, 131 (2d Cir.1974) (reversing order suppressing witnesses’ testimony on the grounds that the Government did not produce witness statements in advance of trial despite being ordered to do so).
The District Court in the instant case, relying on its own opinion in Shvarts, held that where the Government’s obligations under Brady collide with its obligations under the Jencks Act, the former must prevail because the teachings of Brady arise under the Constitution while the Jencks Act is a mere legislative enactment. See Shvarts, 90 F.Supp.2d at 228-29. It is, of course, a fundamental axiom of American law, rooted in our history as a *146people and requiring no citations to authority, that the requirements of the Constitution prevail over a statute in the event of a conflict.
As discussed above, however, the District Court ordered the production of all impeachment evidence without regard for its materiality in the Agurs/Bagley sense. Such an order mandates disclosure of not only those witness statements that fall within the ambit of Brady/Giglio, and thus may be required to be produced in advance of trial despite the Jencks Act, but also those witness statements that, although they might indeed contain impeachment evidence, do not rise to the level of materiality prescribed by Agurs and Bagley for mandated production. As to the latter, a District Court’s power to order pretrial disclosure is constrained by the Jencks Act, see In re United States, 834 F.2d at 286-87, and, therefore, we hold that the District Court exceeded its authority in issuing the February 2, 2001, scheduling order.12
IV. Conclusion
In sum, we hold that
(1) as a general rule, Brady and its progeny do not require immediate disclosure of all exculpatory and impeachment material upon request by a defendant;
(2) material required to be disclosed by Brady and Giglio is material, which, if not disclosed, creates a reasonable probability of altering the outcome;
(3) the Government “suppresses” evidence within the meaning of Brady only if it fails to disclose Brady and Giglio material in time for its effective use at trial or at a plea proceeding; and
(4)the time required for the effective use of a particular item of evidence will depend on the materiality of that evidence as defined by the Supreme Court in Agurs and Bagley, as well as the particular circumstances of the case.
Because the District Court in Shvarts and in this case articulated a general rule of constitutional law requiring the immediate disclosure of all exculpatory and impeachment evidence upon defendants' request-a rule based on a reinterpretation of Brady and its progeny which we reject-we grant the Government's motion for a writ of mandamus and direct the District Court to vacate its February 2, 2001, scheduling order. This case presents no occasion to consider the scope of a trial judge's discretion to order pretrial disclosures as a matter of sound case management. Judge Glasser did not purport to exercise such discretion. We will therefore remand the cause to afford the District Court an opportunity to determine what disclosure order, if any, it deems appropriate as a matter of case management. In so remanding, we intimate no view with respect to the scope of the District Court's case management discretion.
The Government’s petition for a writ of mandamus is granted, and the cause is *147remanded for further proceedings consistent with this opinion.13
. The facts related to those charges are not relevant to this petition.
. On March 15, 2001, the District Court set the start of trial for October 22, 2001.
. "That the obligation of the government to disclose impeachment as well as exculpatory evidence favorable to an accused is an obligation of constitutional dimension is beyond cavil.... It is sufficient to acknowledge, for this purpose, the constitutional obligation, without the necessity to discuss the requirement of 'materiality’ as a precondition to its violation.” Shvarts, 90 F.Supp.2d at 226 (citations omitted).
. The Jencks Act, 18 U.S.C. § 3500, provides in relevant part:
Demands for production of statements and reports of witnesses
(a) In any criminal prosecution brought by the United States, no statement or report in the possession of the United States which was made by a Government witness or prospective Government witness (other than the defendant) shall be the subject of subpena, [sic] discovery, or inspection until said witness has testified on direct examination in the trial of the case.
. Federal Rule of Criminal Procedure 26.2(a) provides:
Motion for Production. After a witness other than the defendant has testified on direct examination, the court, on motion of a party who did not call the witness, shall order the attorney for the government or the defendant and the defendant’s attorney, as the case may be, to produce, for the examination and use of the moving party, any statement of the witness that is in their possession and that relates to the subject matter concerning which the witness has testified.
. Rule 401 of the Federal Rules of Evidence defines "relevant evidence” as "evidence having any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence.” Fed.R.Evid. 401.
. The rules cited by the Supreme Court as requiring more of the prosecution than is required by due process of law are remarkably similar to the rule announced by the District Court in Shvarts and applied by it in this case. Standard 3 3.11(a) provides: "A prosecutor should not intentionally fail to make timely disclosure to the defense, at the earliest feasible opportunity, of the existence of all evidence or information which tends to negate the guilt of the accused or mitigate the offense charged or would tend to reduce the punishment of the accused.” (Emphasis added). Model Rule 3.8(d) provides: "The prosecutor in a criminal case shall ... make timely disclosure of all evidence or information known to the prosecutor that tends to negate the guilt of the accused or mitigates the offense.” (Emphasis added).
. See infra note 9 and accompanying text.
. Amicus Curiae New York Council of Defense Lawyers contends that because guilty pleas are generally made early in pretrial proceedings, our reasoning in United States v. Avellino, 136 F.3d 249, 256, 262 (2d Cir.1998) (relying on Tate v. Wood, 963 F.2d 20 (2d Cir.1992), and Miller v. Angliker, 848 F.2d 1312 (2d Cir.1988)), and United States v. Per-*145sico, 164 F.3d 796, 804 (2d Cir.1999), “strongly suggests that Brady and Giglio disclosures should be made shortly after arraignment,” when plea bargains are usually offered. We do not, however, read those cases to imply anything other than the well-established principle that Brady disclosures must be made in sufficient time for their effective use. In any event, assuming arguendo that those cases do contain such a "suggestion],” they cannot be read to support the District Court’s conclusion that, as a general rule, immediate disclosure of all exculpatory and impeachment material is required to preserve a defendant's constitutional right to due process.
. Congress passed the Jencks Act in response to the Supreme Court’s decision in Jencks v. United States, 353 U.S. 657, 77 S.Ct. 1007, 1 L.Ed.2d 1103 (1957), which held that a criminal defendant had a due process right to inspect, for impeachment purposes, prior statements that a government witness had made to a government agent, see id. at 667-72, 77 S.Ct. 1007. See generally Palermo v. United States, 360 U.S. 343, 345-48, 358-60, 79 S.Ct. 1217, 3 L.Ed.2d 1287 (1959) (discussing the histoxy of the Jencks Act). The Jencks Act was enacted to clarify that the Government need not disclose such statements to the defense until after the Government witness has testified against the defendant on direct examination in open court. See United States v. Covello, 410 F.2d 536, 543 (2d Cir.1969) (citation omitted). It was also adopted in order to limit the application of Jencks to prior "statements” of government witnesses, see 18 U.S.C. § 3500(e) (defining the term "statement”), and to provide an exclusive procedure for the handling of demands by a defendant for the production of such “statements.” See Covello, 410 F.2d at 543. See generally 25 James Wm. Moore et al„ Moore’s Federal Practice § 626.2.03 (2000).
. We also note that in Shvarts and this case the District Court did not purport to order disclosure as a matter of discretion, but rather held, as discussed above, that disclosure on demand was compelled by the Constitution.
. We know that in many cases-perhaps in most cases-prosecutors disclose impeachment materials to a defendant early in the proceedings, without particular regard to the outer limits established by the Jencks Act on when disclosure is required. In recalling today that the Jencks Act provides a set of rules that a prosecutor may invoke to avoid early disclosure of witness statements, we do not intend to limit this often salutary practice, or foreclose other informal arrangements be*147tween parties and the court that reflect the felt necessities of a particular case.
. On May 3, 2001, we granted a stay of the proceedings in the District Court related to this case until further order by this Court. See In re United States, No. 01-3031 (May 3, 2001) (order). We vacate that stay upon the issuance of the mandate.