In the

United States Court of Appeals

For the Seventh Circuit

Nos. 98-2035, 98-2036, 98-2037, 98-2038 & 98-2060

United States of America,

Plaintiff-Appellee,

v.

Jeff Boyd, Charles Green, Sammy Knox,

Noah R. Robinson, and Melvin Mays,

Defendants-Appellants.

Appeals from the United States District Court

for the Northern District of Illinois, Eastern Division.

No. 89 CR 908--James B. Zagel, Judge.

Argued September 27, 1999--Decided April 3, 2000

 Before Posner, Chief Judge, and Ripple and Rovner,

Circuit Judges.

 Posner, Chief Judge. The defendants, members of

Chicago’s "El Rukn" street gang, were indicted

along with other members of the gang in 1989 on a

variety of serious federal charges. They were

tried before a jury in 1991 (all but appellant

Mays) and convicted; but the trial judge (Judge

Aspen) ordered a new trial because the government

had knowingly used false testimony to convict

them and had failed to disclose materials that

the defendants could have used to impeach the

government’s witnesses. After we affirmed his

order, 55 F.3d 239 (7th Cir. 1995), the

defendants were retried, this time before Judge

Zagel, and at the end of the 12-week trial the

jury again convicted the defendants (now

including Mays) of multiple crimes--mainly

narcotics violations, and murders committed in

the course of turf wars with rival drug gangs--

all pursuant to a continuing and wide-ranging

conspiracy reaching back to the mid-1960s. All

five defendants were sentenced to life

imprisonment except Boyd, who was sentenced to 50

years.

 The appeals present almost 20 separate issues,

but we confine our discussion to those that have

at least colorable merit. Although all the

appellants are represented by counsel, Robinson

has filed a pro se supplemental brief. Earlier

motions by him to file such a brief were
repeatedly denied. Eventually the presiding judge

of this panel allowed it to be filed; but on

further consideration, given the lateness of the

filing (long after the case was argued), we have

decided to vacate the order allowing the brief to

be filed. It goes without saying that a

represented litigant has no right to file a pro

se brief, e.g., United States v. Gwiazdzinski,

141 F.3d 784, 787 (7th Cir. 1998), and although

we can permit such a filing in appropriate

circumstances, e.g., Hayes v. Hawes, 921 F.2d

100, 101-02 (7th Cir. 1990) (per curiam), given

the lateness of the filing and the repetitive

character of the motion the circumstances are not

appropriate.

 At the first trial--the one set aside because of

prosecutorial misconduct--Edgar Cooksey was a

defendant and he was convicted with the others.

But after the new trial was ordered, he pleaded

guilty, and he testified for the government at

the second trial. The examination of Cooksey both

by the government’s lawyer and by one of the

defense lawyers, which was conducted over a

period of three days, brought out the fact that

Cooksey had been a codefendant of at least some

of the current defendants, that they had been

indicted in 1989, that he had testified at a

previous jury trial in 1991 called "United States

v. Boyd" (which the current jury knew, of course,

was the title of the case it was hearing), that

he had spoken to the judge in that trial in

"allocution" and had "accepted responsibility"

for his acts, that he had pleaded guilty shortly

before the beginning of the current trial, and

that he had been in prison continuously since

1991. The lawyers for the other defendants thrice

objected to the questions that elicited this

information, and moved for a mistrial on the

ground that the jury was bound to infer that the

defendants had been convicted by a previous jury.

The government concedes that it can be a

reversible error to disclose to the jury (or

allow the jury to discover) that a defendant was

previously convicted by another jury, see, e.g.,

United States v. O’Keefe, 722 F.2d 1175, 1179

(5th Cir. 1983); United States v. Attell, 655

F.2d 703, 705-06 (5th Cir. 1981); United States

v. Williams, 568 F.2d 464, 470-71 (5th Cir.

1978), though reversal is not automatic. Patton

v. Yount, 467 U.S. 1025, 1031-35 (1984); United

States v. Keating, 147 F.3d 895, 900 (9th Cir.

1998); cf. United States v. Bruscino, 687 F.2d

938, 940 (7th Cir. 1982) (en banc); United States

v. Plescia, 48 F.3d 1452, 1464-65 (7th Cir.

1995). And reversal is out of the question--no

possible prejudice is shown--if the damning fact

is not actually disclosed. Judge Zagel refused to

grant a mistrial, saying he thought it unlikely

that the jury would infer that the defendants had
previously been found guilty; if he was right,

the question whether the jury could have set

aside their knowledge of the fact would not even

arise.

 The question of what the jury is likely to have

inferred from statements made in its presence,

like the question whether the jury is likely to

have been prejudiced by hearing things they

shouldn’t have, Marshall v. United States, 360

U.S. 310, 312 (1959) (per curiam); United States

v. Bruscino, supra, 687 F.2d at 940-41; United

States v. Zizzo, 120 F.3d 1338, 1349 (7th Cir.

1997), is quintessentially one for the trial

judge to answer, subject only to light appellate

review. Because he has his finger on the pulse of

the trial and monitors the alertness and

attentiveness of the jury, he is in a better

position than the appellate judges to determine

whether prejudicial matter presented at the trial

is likely to have affected the outcome. Judge

Zagel could tell how the jurors seemed to be

"taking" the revelations concerning Cooksey’s

previous trial. In the circumstances, we do not

think he abused his discretion in refusing to

grant a mistrial. The revelations had been

scattered over three days of examination and

cross-examination of Cooksey and, since they

employed technical legal terminology (such as

"allocution") and were thus susceptible of other

interpretations by a jury of lay persons, did not

compel an inference that the current defendants

had previously been convicted.

 The next issue concerns the admissibility of

tape recordings of telephone conversations in

1985 and 1986 in which the defendants made

incriminating admissions. The defendants argue

that the reliability of the recordings was never

adequately determined, that some may have been

tampered with, and that the government violated

the Brady rule by failing to disclose a specific

problem with the accuracy of the tapes that could

have been used to impeach the government’s

evidence. Brady v. Maryland, 373 U.S. 83 (1963).

Because tape recordings at once are devastatingly

effective evidence and are susceptible to

tampering that is very difficult to discover,

Title III--the federal statute that regulates

electronic surveillance--requires that recordings

"be done in such way as will protect the

recording from editing or other alterations." 18

U.S.C. sec. 2518(8)(a). To this end, the section

requires that the recordings be judicially sealed

as soon as the interception order pursuant to

which they were made expires. Id.; United States

v. Ojeda Rios, 495 U.S. 257, 263 (1990); United

States v. Jackson, No. 98-2696, 2000 WL 248575,

at *3 (7th Cir. March 23, 2000); United States v.

Plescia, supra, 48 F.3d at 1463; United States v.
Wong, 40 F.3d 1347, 1375 (2d Cir. 1994). This was

done here, back in 1985 and 1986. The original

recordings were placed in sealed envelopes, and

the envelopes in sealed boxes. Some of the seals,

both on boxes and on envelopes, were later

broken, and anyway the recordings that were

actually placed in evidence were not the original

recordings. They were copies of duplicate

originals made at the same time as the original

recordings and intended to be identical to them.

They differed--or at least were supposed to

differ--only in having been made on a different

machine, recording the same conversations.

Neither the duplicate originals nor the copies

made from them were secured against tampering.

 The admissibility of the copies was not

challenged at the first trial, and the district

judge ruled that this waived the issue as to all

the appellants but Mays, who was not a defendant

at that trial. The judge was wrong. Rulings made

at a previous trial of the same case only

presumptively control the second trial, under the

doctrine of law of the case, Alston v. King, 157

F.3d 1113, 1116 (7th Cir. 1998), and when the

ruling concerns the admissibility of evidence the

presumption is either nonexistent, Tang v. Rhode

Island, 163 F.3d 7, 11 (1st Cir. 1998); United

States v. Akers, 702 F.2d 1145, 1147-48 (D.C.

Cir. 1983), or weak, Menzer v. United States, 200

F.3d 1000, 1004-05 (7th Cir. 2000); United States

v. Williams, 2000 WL 204531, at *11 (2d Cir. Feb.

23, 2000); United States v. Todd, 920 F.2d 399,

403 (6th Cir. 1990); United States v. Birney, 686

F.2d 102, 107 (2d Cir. 1982), since issues of

admissibility are often highly contextual and

evidence at a second trial will often deviate

significantly from that at the first. See, e.g.,

Coal Resources, Inc. v. Gulf & Western

Industries, Inc., 954 F.2d 1263, 1265-66 (6th

Cir. 1992). (The presumption is strongest when

the ruling concerns a rule of law, and some cases

might be taken to suggest that it operates only

then. Arizona v. California, 460 U.S. 605, 618

(1983); Payne v. Churchich, 161 F.3d 1030, 1037

n. 8 (7th Cir. 1998).) Even the Ninth Circuit,

which takes a harder line on the binding effect

of evidentiary rulings made in the first trial,

United States v. Tham, 960 F.2d 1391, 1397-98

(9th Cir. 1991), does not regard failure to

object at the first trial as an irrevocable

waiver. Id. at 1398; United States v. Seidman,

503 F.2d 1027 (9th Cir. 1974). The judge’s error

in supposing the defendants absolutely precluded

from challenging the admissibility of the copies

at the second trial was peculiarly harmless,

however, since he had to discuss the merits of

the issue of admissibility with regard to Mays,

and that discussion is equally applicable to the

admissibility of the tape recordings against the
other defendants. And so let us turn to those

merits.

 The fact that the recordings used at the trial

had not been sealed was not, as the defendants

argue, fatal; nor the fact that the seals had

been broken (the seals have to be broken at some

point, if the recordings are to be placed in

evidence). Neither Title III nor the case law

places specific restrictions on the manner in

which the contents of tape-recorded conversations

can be communicated to the jury at trial. See 18

U.S.C. sec. 2517(3); United States v. Rivera, 153

F.3d 809, 812 (7th Cir. 1998). The relevant

issues are, rather, whether Title III permitted

the disclosure of the contents of the

conversations at all, and whether (if so) the

particular evidence conveying those contents to

the jury was adequately authenticated.

 The contents of a recorded communication

governed by Title III can lawfully be disclosed

even if the recording was not under seal,

provided the absence of the seal is

satisfactorily explained. 18 U.S.C. sec.

2518(8)(a); cf. United States v. Jackson, supra,

at *3. The usual satisfactory explanation is a

judicial order unsealing the recording so that it

can be used in evidence, and such orders were

indeed issued here for both sets of tapes that

are at issue. In the case of successive trials,

as we have here, the recording should be resealed

after the first trial, United States v. Long, 917

F.2d 691, 699-700 (2d Cir. 1990); United States

v. Scopo, 861 F.2d 339, 347 (2d Cir. 1988)--and

promptly, too. But this was done. Although

defendants argue--belatedly, in their reply

brief, Employers Ins. of Wausau v. Browner, 52

F.3d 656, 665-66 (7th Cir. 1995)--that one set of

tapes had been unsealed for the nine years since

the first trial, the trial judge was entitled to

and did credit the contrary testimony of the

government agent who examined them in preparation

for the second trial.

 But it is not the case that these recordings

were merely removed from the boxes and envelopes

pursuant to judicial order and played to the

jury; they were not played to the jury at all;

copies were played to the jury and the second and

separate issue concerning their admissibility is

whether the copies were adequately authenticated.

On this issue two types of evidence were

presented that the judge found convincing. First,

one of the turncoat witnesses, Jackie Clay,

testified that a recording of a telephone

conversation that he had participated in back in

1986 was accurate. Although testifying ten years

later Clay could hardly have been certain about

the matter--any pretense of certainty would
merely have cast doubt on his credibility--

participants in other recorded conversations who

testified for the government were not asked by

the defendants’ lawyers whether the recordings

were accurate. The district judge inferred from

testimony by government agents that the other

conversations had been recorded in like manner to

the one Clay testified about and, from the

absence of any contrary evidence, that the

recordings of those conversations were probably

accurate too. Second, a government agent

testified that he opened some of the sealed

evidence envelopes pursuant to an unsealing order

by the district judge and compared the tapes in

them to the tapes played at trial, and found no

discrepancies.

 Clay’s testimony was weak because of the lapse

of time. The agent’s was stronger, although not

airtight. For one thing, he didn’t compare all

the tapes played at trial with the originals.

Rather, he conducted a spot check, and having

discovered no discrepancies in the tapes that he

sampled decided not to check further. For

another, there is an unexplained discrepancy

between one of the original recordings and its

duplicate original, which although supposed to be

identical contained conversations not audible on

the original. The expert who examined the two

tapes could not determine the cause of the

discrepancy. It could have been a malfunction, or

it could have been a bit of creative editing, but

the latter inference, as the judge determined,

was the less likely, precisely because the

duplicate contained more conversation than the

original. It was the duplicate that was used in

evidence, and if the government had edited out

portions that favored the defendants, the

original would have had more conversation than

the duplicate. Although it is possible in

principle that the government "edited in"

additional conversation to the duplicate, there

is no indication at all of this more elaborate

form of tampering. Similarly, while it would have

been preferable had the agent checked all the

tapes, no reasons have been suggested for

doubting either the good faith or the adequacy of

his sampling.

 It is essential to distinguish between excluding

evidence for want of adequate authentication, and

challenging its weight. The defendants were

entitled to and did question the weight that the

jury should give the tape recordings in light of

the possibility of tampering, but questions of

authentication are governed by Fed. R. Evid.

901(a), which merely requires "evidence

sufficient to support a finding that the matter

in question is what its proponent claims," that

is, that the recordings played to the jury were
in fact recordings of the defendants’

conversations. Testimony by an "ear" witness,

such as Clay, is sufficient, United States v.

Brown, 136 F.3d 1176, 1182 (7th Cir. 1998); there

is more here; and we have said in previous cases

that only in "extraordinary" circumstances will

we reverse the trial judge’s decision to admit

tape recordings over objections based on lack of

authentication. United States v. Magana, 118 F.3d

1173, 1207 (7th Cir. 1997); United States v.

Welch, 945 F.2d 1378, 1383 (7th Cir. 1991);

United States v. Vega, 860 F.2d 779, 788 (7th

Cir. 1988). That high standard is not met here.

 The Brady rule requires the government to

disclose evidence it knows about that would be

helpful to the defense, whether because the

evidence is exculpatory or because it could be

used to impeach the government’s evidence. Brady

v. Maryland, supra, 373 U.S. at 87; Strickler v.

Greene, 119 S. Ct. 1936, 1948 (1999). The

discrepancy between one of the original tapes and

its duplicate, a discrepancy that could have been

used to some effect to impeach the government’s

taped evidence, may have arisen as early as 1986,

when the two recordings were made; in any event

it was not recent, and the defendants ask us to

infer from this that the government must have

known about it. But of this there is no other

evidence and the inference is implausible because

the government prepared its case from the

duplicate originals while the "original

originals" remained in storage. So far as

appears, the discrepancy was first discovered by

the defendants, who thought they heard something

odd on one of the tapes; they drew this to the

judge’s attention and then the comparison was

conducted, which confirmed the existence of the

anomaly. Brady liability is not strict; the

government does not violate Brady by failing to

disclose information that it (or its agents,

e.g., Kyles v. Whitley, 514 U.S. 419, 437 (1995)-

-a category that doesn’t include the criminal

defendants whom it prosecutes!) doesn’t know

about. United States v. Bhutani, 175 F.3d 572,

577 (7th Cir. 1999); United States v. Earnest,

129 F.3d 906, 910 (7th Cir. 1997); United States

v. Avellino, 136 F.3d 249, 255 (2d Cir. 1998).

The discrepancy between the tapes is such

information.

 We come last to the most troubling issue in the

case--whether Judge Zagel should have

disqualified himself from presiding at this

trial. We have already held, in another case

involving the El Rukns, that Judge Zagel’s

refusal to disqualify himself was not a plain

error, United States v. Franklin, 197 F.3d 266,

270 (7th Cir. 1999), but the question remains

whether it was error. There is a threshold
procedural question, which is both novel and

unnecessary to resolve. Section 144 of the

Judicial Code entitles a party to disqualify a

judge (only once per case, however) on the basis

just of an affidavit sufficiently alleging the

existence of a personal bias or prejudice in

favor of an adverse party or against the affiant;

but the affidavit must be "accompanied by a

certificate of counsel of record stating that it

is made in good faith." Defendant Robinson filed

a section 144 affidavit against Judge Zagel, but

without the required certificate, because

Robinson was proceeding pro se. The judge ruled

that the absence of the certificate was fatal.

The ruling denies pro se parties the benefit of

the statute, a result that might be thought an

undue burden on the constitutional right of a

criminal defendant to proceed pro se. Faretta v.

California, 422 U.S. 806, 834, 836 (1975); United

States v. Brock, 159 F.3d 1077, 1079 (7th Cir.

1998); see also 28 U.S.C. sec. 1654. Yet the

requirement of the certificate is salutary, given

that the statute makes the party’s affidavit

conclusive for recusal provided it alleges the

requisite bias or prejudice. The obvious

solution, suggested by Robinson himself but

opposed by the government and rejected by the

judge, is to appoint a lawyer for the pro se

defendant for the limited purpose of enabling him

to determine whether to file the certificate. The

rejection of this measure--a measure we commend

to the district courts in future cases--turns out

to have been harmless, however, because the

relevant facts in Robinson’s affidavit were

conceded.

 Section 455(a) of the Judicial Code requires a

judge to disqualify himself "in any proceeding in

which his impartiality might reasonably be

questioned." Our cases hold that appellate review

of a judge’s refusal to disqualify himself under

this section is possible only by petitioning the

appellate court for mandamus before trial. E.g.,

In re Hatcher, 150 F.3d 631, 637 (7th Cir. 1998);

United States v. Horton, 98 F.3d 313, 316-17 (7th

Cir. 1996); Taylor v. O’Grady, 888 F.2d 1189,

1201 (7th Cir. 1989); United States v.

Balistrieri, 779 F.2d 1191, 1204-05 (7th Cir.

1985). This is a minority position, see, e.g., In

re Cargill, Inc., 66 F.3d 1256, 1264 and n. 10

(1st Cir. 1995); United States v. Cooley, 1 F.3d

985, 996 n. 9 (10th Cir. 1993); In re School

Asbestos Litigation, 977 F.2d 764, 777 n. 12 (3d

Cir. 1992); Chitimacha Tribe v. Harry L. Laws

Co., 690 F.2d 1157, 1164 n. 3 (5th Cir. 1982),

but the defendants do not ask us to reexamine it.

On the contrary, they expressly waive any

challenge to the rule by stating in their

consolidated brief that "the motion for recusal

under 28 U.S.C. sec. 455(a) could only be, and
was, appealed by mandamus." Given this express

waiver by experienced counsel, it would be

inappropriate for us to reexamine the rule in

this case.

 Because the rule forecloses appellate review at

the conclusion of the case, we review a petition

for mandamus to enforce section 455(a) under the

normal appellate standard. Hook v. McDade, 89

F.3d 350, 353-54 and n. 3 (7th Cir. 1996). Such a

petition was filed here, and another panel of

this court denied it, but in an unpublished order

with no statement of reasons, a disposition that

we find puzzling because, as will soon become

clear, the case for disqualification under

section 455(a) was more than colorable, and

indeed in our judgment was compelling. But there

is no reason to suppose that the panel which

denied mandamus applied the incorrect standard,

and in the absence of such an error we cannot

revisit the issue without abandoning the rule

that makes mandamus the exclusive route for

challenging a judge’s refusal to disqualify

himself under section 455(a).

 The defendants also argue, however, that Judge

Zagel should have disqualified himself under

either of two other subsections (or both) of

section 455. The first is (b)(1), which so far as

bears on this case requires disqualification if

the judge has "personal knowledge of disputed

evidentiary facts concerning the proceeding." The

second is (b)(3), which requires disqualification

if the judge had, when he was a government

employee, "participated as counsel, adviser or

material witness concerning the proceeding or

expressed an opinion concerning the merits of the

particular case in controversy."

 In 1983, at which time the now-Judge Zagel was

the head of the Illinois state police, Robinson

opened a restaurant in Chicago. Late in 1985 or

early in 1986, when Zagel was still head of the

state police, Robinson hired security guards for

his restaurant from a company called Security &

Maintenance Service (SMS), which was owned and

operated by El Rukn "General" Hunter, a key

government witness at the 1996 trial here on

appeal. These guards were unarmed but SMS had

applied for a license that would permit them to

be armed. The El Rukns’ purpose in operating a

security agency whose employees were authorized

to carry weapons was, of course, to strengthen

the gang’s position in the endless turf wars in

the course of which the murders with which these

defendants were charged were committed. The

authorities got wind of the scheme. They were

already investigating the El Rukns (whose drug

and related criminal activities went back to the

1960s, remember) by means of a joint federal,
state, and local task force that included members

of the Illinois state police. The task force

conducted a "sting" of SMS. An Illinois state

police officer played a key role in the sting,

operating undercover and dealing directly with

Hunter and Robinson. In June of 1986, Chicago

police officers who were members of the task

force and who later worked on the present case

raided SMS’s premises, which Robinson owned, and

arrested (at another location) 18 of its

employees. One of them, Crowder, was a defendant

in the first trial of this case and a defense

witness in the second trial, the trial before

Judge Zagel.

 The day of the arrest, Director Zagel held a

joint press conference with Richard Daley, at the

time the Cook County prosecutor. They announced

the arrests and explained that they had begun

investigating SMS when they learned that Crowder,

an El Rukn "captain," had applied for a state

firearm identification card. Zagel remarked that

"street gangs [such as the El Rukns] have grown

to rival organized crime in the scope of their

operations, and in the savagery in which they

control entire sections of the city." The El

Rukns task force produced the evidence that led

to the 1989 indictments of the present

defendants. Not only did two of the El Rukns who

had been involved in the SMS caper testify at the

trial before Judge Zagel, but they testified--

Hunter extensively--about the caper, using it to

tie Robinson to other El Rukn activities as well.

 In denying the motion to recuse, Judge Zagel

said that the SMS investigation had had nothing

to do with the current trial, but this is

incorrect. The creation of SMS was part of the

drug and incidental murder conspiracy for which

the defendants in the present case were tried and

convicted before Judge Zagel, although SMS’s

activities were not charged as overt acts of the

conspiracy. The judge was involved in the

investigation of activities at issue in the

trial, and the press conference shows that he had

personal, extrajudicial knowledge of those

activities. But SMS’s activities were not at

issue in this case except insofar as they

connected Robinson to the El Rukns. Had Judge

Zagel learned of this connection from the 1986

investigation of SMS, Robinson would be entitled

to a new trial before a different judge. But

Zagel did not mention Robinson at the press

conference, and there is no basis in the record

for Robinson’s claim that Zagel was the "point

man" for the investigation and had "full

knowledge" of its details. The judge denied this

charge on the record, and in the absence of

contrary evidence (Robinson’s mere assertion not

being evidence), we must credit the denial.
United States v. Balistrieri, supra, 779 F.2d at

1202.

 This conclusion is only superficially in tension

with our (and Judge Zagel’s) crediting the facts

alleged in Robinson’s affidavit in support of his

motion to recuse Judge Zagel under 28 U.S.C. sec.

144. The only facts in such an affidavit that

must be credited, and plainly the only facts in

Robinson’s affidavit that Judge Zagel did credit,

are those that are "sufficiently definite and

particular to convince a reasonable person that

bias exists; simple conclusions, opinions, or

rumors are insufficient." United States v. Sykes,

7 F.3d 1331, 1339 (7th Cir. 1993); see also

United States v. Balistrieri, supra, 779 F.2d at

1199; Jones v. Pittsburgh Nat’l Corp., 899 F.2d

1350, 1356 (3d Cir. 1990); 13A Charles Alan

Wright, Arthur R. Miller & Edward H. Cooper,

Federal Practice and Procedure sec. 3551, pp.

634-37 (2d ed. 1984). Robinson’s assertions that

Zagel was the "point man" of the investigation

and had "full knowledge" of the details of the

investigation don’t count as factual assertions;

they are conclusions.

 Section 455(b)(3) is also inapplicable. Zagel

did not participate other than as judge in the

present case and did not, back when he was head

of the state police, express an opinion about it.

The case was then, of course, years in the

future. There is a pregnant difference in wording

between the participation and expression-ofopinion clauses of 455(b)(3). The former refers

to participation in "the proceeding," the latter

to expressing an opinion on the merits of "the

particular case in controversy," and we have held

that the use of the word "particular" narrows the

clause to the situation in which the judge

expressed his opinion in "the present case, not a

related former case." Russell v. Lane, 890 F.2d

947, 948 (7th Cir. 1989); cf. Rice v. McKenzie,

581 F.2d 1114, 1116 (4th Cir. 1978). In any

event, since nothing Zagel said at the press

conference could reasonably be construed as an

expression of opinion on the merits of the case

that he presided over, we need not pursue this

novel and interesting interpretive question.

 The cases interpreting the participation clause

do not require a formal identity between the

proceeding in which the government employee who

is now a judge participated or expressed an

opinion about; it is enough if they overlap

significantly. See, e.g., United States v.

Outler, 659 F.2d 1306, 1312-13 (5th Cir. 1981);

Jenkins v. Bordenkircher, 611 F.2d 162, 166 (6th

Cir. 1979); Mixon v. United States, 608 F.2d 588,

591-92 (5th Cir. 1979). And there was an overlap

here, in the part of the SMS investigation that

linked Robinson to the El Rukns. But Director
Zagel never expressed an opinion about that

aspect of the investigation, and the requisite

"participation" is not imputed to a supervisor by

virtue of his supervisory authority; it must be

personal, and it was not. E.g., Mangum v.

Hargett, 67 F.3d 80, 83 (5th Cir. 1995); Kendrick

v. Carlson, 995 F.2d 1440, 1444 (8th Cir. 1993);

United States v. Di Pasquale, 864 F.2d 271, 279

(3d Cir. 1988). The exception noted in the lasttwo cited cases for where the supervisor is the

U.S. Attorney is not applicable here.

 Recurring briefly to section 455(a), we wish to

emphasize our belief that compliance with it is

essential to the perceived legitimacy of the

judicial process, especially when the defendants

are vicious criminals facing long sentences and

the prosecution has been marred by

irregularities. It would have been far, far

better for Judge Zagel to have recused himself in

light of his earlier involvement with the

parallel proceeding against the El Rukns and the

fact that two of the El Rukns involved in that

proceeding testified in the present case. But the

panel that considered the petition for mandamus

ruled that there was no violation of section

455(a), and while we disagree with the ruling,

the issue of its soundness is not before us.

 Several sentencing issues remain to be

discussed. Green and Mays argue that their

sentences violate the ex post facto clause, U.S.

Const., art. I, sec. 9, cl. 3, because the

conspiracies did not persist beyond the date on

which the statutes under which they were

sentenced were enacted or because they had

withdrawn from the conspiracies prior to that

date. The first claim is just wrong, for although

there wasn’t a great deal of evidence of

continued drug dealing by the El Rukns subsequent

to the crucial dates (November 1, 1987, for one

of the statutes under which these defendants were

sentenced and November 18, 1988, for another),

there was enough to place the district judge’s

finding beyond possibility of reversal for clear

error. Withdrawal from a conspiracy requires a

definitive break, rather than mere cessation of

activities even when combined with a subjective

determination not to resume; otherwise a

conspirator could sit back and wait to see

whether the conspiracy had succeeded or failed

and only then decide whether to announce that he

had withdrawn. E.g., United States v. Wilson, 134

F.3d 855, 863 (7th Cir. 1998); United States v.

Williams, 81 F.3d 1434, 1442 (7th Cir. 1996);

United States v. Diaz, 176 F.3d 52, 98 (2d Cir.

1999). Mays’s argument that he withdrew when he

became a fugitive from justice borders on the

frivolous, United States v. Pandiello, 184 F.3d

682, 687 (7th Cir. 1999), as it would merely

reward fugitives; and anyway there is nothing
about hiding to suggest withdrawal--Mays was

hiding from the police rather than from the El

Rukns.

 Green has a better argument, that he could not

be given a sentencing enhancement for having been

a leader of the conspiracy (U.S.S.G. sec.

3B1.1(a)) when his leadership role had--and this

the government acknowledges--ended with his

demotion from El Rukn "General" to private before

the guideline under which his sentence was

enhanced went into effect (as one of the original

guidelines) on November 1, 1987. The conspiracy

of which he was a member straddled the date of

promulgation, and a crime that straddles can be

punished under a guideline promulgated after the

straddle date. E.g., United States v. Kramer, 955

F.2d 479, 485 (7th Cir. 1992); United States v.

Hargus, 128 F.3d 1358, 1365 (10th Cir. 1997), and

United States v. Smith, 46 F.3d 1223, 1239 (1st

Cir. 1995). The straddle rule implies punishment

for conduct committed before the date of the

guideline that determined the severity of the

punishment, and we cannot see what difference it

can make whether the pre-guideline conduct was

the sale of a quantity of drugs perhaps much

greater than any that occurred after the critical

date or the exercise of leadership

responsibilities relinquished by that date.

 Green’s best case is United States v. Torres,

901 F.2d 205, 226-27 (2d Cir. 1990), which held

that the ex post facto clause forbids punishing

the defendants as "principal administrators,

organizers, or leaders" of a continuing criminal

enterprise if their leadership role did not

continue after the enactment of the statute

creating the offense, even though the enterprise

itself did continue past that date. See also

United States v. Williams-Davis, 90 F.3d 490,

510-11 (D.C. Cir. 1996) (acknowledging but

distinguishing Torres). The statute at issue in

Torres created a new substantive offense that

required as one of its elements that the

defendant have had a leadership role, and so

punished Torres for engaging in conduct before

the statute was passed. In our case the defendant

committed all the elements of the offense after

the change in the sentencing guideline and by

doing so became responsible for the conduct in

which he had engaged before the change. Torres

was not a straddle case; ours is; if the

difference seems tenuous, then we must reject

Torres, as we are committed to the straddle

doctrine--and so, for that matter, is the Second

Circuit, which reaffirmed the straddle doctrine

in Torres itself. We add that Green could have

avoided the new guideline by quitting the

conspiracy when the guideline was announced but

before it took effect.
 Last, we note some clerical mistakes in the

judgments. Mays’s judgment should reflect a

guidelines life sentence on count 3 and 60 months

on count 4, rather than vice versa, and Green’s

judgment should reflect a life sentence on counts

1 and 3 and concurrent 10-year terms on counts 4

and 5, rather than a life sentence on counts 1,

4, and 5 and a 10-year sentence on count 3. As

modified to correct these mistakes, the judgments

are

Affirmed.

 RIPPLE, Circuit Judge, dissenting. The panel is

unanimous in its view that the trial judge should

have recused himself under sec. 455(a), which

requires a judge to "disqualify himself in any

proceeding in which his impartiality might

reasonably be questioned." Under the

circumstances set forth in detail by the majority

here, in any other circuit a new trial would be

ordered. In this circuit, however, we can only

review the trial judge’s decision against recusal

when the issue is presented in a petition for a

writ of mandamus. The defendants did file a

petition for mandamus relief from the trial

judge’s decision not to recuse himself, and

another panel of this court denied that petition

without opinion.

 The rule that mandamus is the only avenue by

which a party can seek review of a ruling under

sec. 455(a) is well-established in this circuit.

See United States v. Horton, 98 F.3d 313, 316-17

(7th Cir. 1996); Hook v. McDade, 89 F.3d 350, 353

n.2 (7th Cir. 1996); United States v. Towns, 913

F.2d 434, 443 (7th Cir. 1990). This circuit’s

view has been that sec. 455(a) is intended to

protect against the appearance of impropriety,

and that, once the proceedings in the district

court have been completed, the harm sec. 455(a)

seeks to prevent has already occurred. See United

States v. Troxell, 887 F.2d 830, 833 (7th Cir.

1989). Thus, we have required litigants to bring

mandamus petitions to cure potential problems

under sec. 455(a) and to prevent a potentially

tainted trial from ever taking place. See id.

 No other court of appeals has followed our

approach. See Kenneth M. Fall, Note, Liljeberg v.

Health Services Acquisition Corp.: The Supreme

Court Encourages Disqualification of Federal

Judges Under Section 455(a), 1989 Wis. L. Rev.

1033, 1056. Some circuits have rejected

explicitly our position. The Third Circuit has
said that mandamus is the preferred method of

appeal, but allows review on direct appeal

because it may provide a "partial cure" to any

harm to the public perception of the judiciary.

See In re School Asbestos Litig., 977 F.2d 764,

777 n.12 (3d Cir. 1992). The Tenth Circuit has

held that, although sec. 455(a) is concerned with

the rights of the public, the parties do retain

some rights thereunder, and direct appeal may

therefore be appropriate. See United States v.

Cooley, 1 F.3d 985, 996 n.9 (10th Cir. 1993).

Other circuits have entertained sec. 455(a)

arguments on direct appeal and, indeed, have

addressed the merits or found the issue waived

because it was not raised in the district court.

See, e.g., United States v. Mosby, 177 F.3d 1067,

1068-69 (8th Cir. 1999); United States v.

Morrison, 153 F.3d 34, 48-49 (2d Cir. 1998);

United States v. Barrett, 111 F.3d 947, 951-53

(D.C. Cir. 1997); United States v. Sturman, 951

F.2d 1466, 1481-82 (6th Cir. 1991); Diversified

Numismatics, Inc. v. City of Orlando, 949 F.2d

382, 384-85 (11th Cir. 1991) (per curiam); United

States v. Arache, 946 F.2d 129, 140 (1st Cir.

1991); United States v. Payne, 944 F.2d 1458,

1476-77 (9th Cir. 1991); United States v. Wade,

931 F.2d 300, 302-05 (5th Cir. 1991); United

States v. Mitchell, 886 F.2d 667, 671 (4th Cir.

1989).

 Moreover, we not only stand alone among the

circuits in our approach to this question, but we

also have taken a position in considerable

tension with the decisions of the Supreme Court

of the United States. Indeed, the Supreme Court

appears to have taken a different path. Although

the Court has not rejected explicitly that

mandamus is the only avenue of review for sec.

455(a) matters, it has twice interpreted that

section in cases brought to it in the manner of

an appeal from final judgment. See Liteky v.

United States, 510 U.S. 540 (1994); Liljeberg v.

Health Services Acquisition Corp., 486 U.S. 847

(1988). These cases, especially Liljeberg’s

approval of vacatur of a trial court’s judgment,

clearly cast significant doubt on our view that

mandamus is the only appropriate remedy under

sec. 455(a). Nevertheless, we never have

considered whether these decisions of the Supreme

Court make our approach untenable; we have

continued to follow our same approach even after

the announcement of those Supreme Court

decisions. 

 This case points out one of the pitfalls of our

approach. As the Third Circuit has suggested, a

trial judge well might appear unbiased at the

outset of a trial, but later events might cause a

judge’s impartiality to be reasonably questioned

and thus make appropriate the "partial cure" of
reversing the improperly obtained verdict.

Asbestos Litig., 977 F.2d at 777-78. Indeed, in

one recent case, the First Circuit, although

denying mandamus relief, specifically left open

the possibility that further development of the

record could lead to a different conclusion on an

appeal from final judgment. See In re MartinezCatala, 129 F.3d 213, 221 (1st Cir. 1997).

Regardless of whether this panel would have

issued the same ruling as the earlier motions

panel if it had been presented with the record

available at that early stage of the litigation,

the record made at trial has convinced us that

recusal is necessary. There must be public

confidence in a judgment that incarcerates

defendants, in some cases for the rest of their

lives. The trial of this matter was a difficult

task. It required that the trial court make many

rulings, both with respect to the admissibility

of evidence and the enhancement of sentences,

that required the exercise of a great deal of

discretion.

 After thorough review of the record, this panel

believes that the district judge should have

recused himself under 28 U.S.C. sec. 455(a). Only

our rigid adherence to a procedural rule not

followed in any other circuit and in significant

tension with the decisions of the Supreme Court

of the United States prevents our giving the

relief that, under the prevailing national

standards, would be granted. See, e.g., United

States v. Bremers, 195 F.3d 221 (5th Cir. 1999)

(vacating conviction because trial judge should

have recused himself under sec.455(a)); Cooley, 1

F.3d at 998 (same); United States v. Brown, 539

F.2d 467 (5th Cir. 1976) (same). See also United

States v. Waskom, 179 F.3d 303, 315-16 (5th Cir.

1999) (vacating sentence in guilty plea case even

in the absence of specific allegation of

sentencing error because trial judge should have

recused himself); United States v. Reyes, 160

F.3d 258, 259 (5th Cir. 1998) (vacating sentence

in guilty plea case because of failure to

recuse).

 The majority characterizes the defendants’

reference to the earlier mandamus proceeding as a

waiver of the argument that mandamus should not

be the only available remedy. The defendants

state: "Defendants appeal the denial of recusal

under 28 U.S.C. sec.sec. 144 and 455(b). The

motion for recusal under 28 U.S.C. sec. 455(a)

could only be, and was, appealed by mandamus."

Appellant’s br. at 49. This was sufficient to put

this court on notice of our rule that only

mandamus relief is available under sec. 455(a).

It is indeed a parsimonious reading of this

statement to characterize it as a knowing and

intelligent waiver. Far from ignoring the issue,
the defendants specifically brought it to our

attention. Because the defendants raised the

matter, and clearly have maintained throughout

this litigation that recusal under sec. 455(a)

was required, this court should not be restrained

from reconsidering in this case our position on

the issue./1

 Moreover, even if the defendants did not raise

this issue, we are in no way precluded from

raising it on our own in the interests of

justice. The Supreme Court has acknowledged that

it often decides cases on issues other than those

argued fully by the parties:

"On a number of occasions, this Court has

considered issues waived by the parties below and

in the petition for certiorari because the issues

were so integral to decision of the case that

they could be considered ’fairly subsumed’ by the

actual questions presented." Gilmer v.

Interstate/Johnson Lane Corp., 500 U.S. 20, 37,

111 S. Ct. 1647, 114 L.Ed.2d 26 (1991) (Stevens,

J., dissenting) (citing cases). The court has not

always confined itself to the set of issues

addressed by the parties.

Kolstad v. American Dental Assoc., 119 S.Ct.

2118, 2127 (1999). The Court has also

specifically instructed the courts of appeals

that they, too, may raise issues on their own

initiative:

The matter of what questions may be taken up and

resolved for the first time on appeal is one left

primarily to the discretion of the courts of

appeals, to be exercised on the facts of

individual cases. We announce no general rule.

Certainly there are circumstances in which a

federal appellate court is justified in resolving

an issue not passed on below, as where the proper

resolution is beyond any doubt, or where

injustice might otherwise result.

Singleton v. Wulff, 428 U.S. 106, 121 (1976)

(citations and quotations omitted); see also

Niedert v. Rieger, 200 F.3d 522, 527 (7th Cir.

1999) (quoting Singleton); United States v.

Brown, 739 F.2d 1136, 1145 (7th Cir. 1984)

(same).

 Prior to Singleton, the Ninth Circuit explained

the circumstances that might motivate a court of

appeals to address a matter without the benefit

of full briefing by the parties:

There is . . . no rigid and undeviating

judicially declared practice under which courts

of review invariably and under all circumstances

decline to consider all questions which have not
previously been specifically urged. Indeed there

could not be without doing violence to the

statutes which give federal appellate courts the

power to modify, reverse or remand decisions as

may be just under the circumstances. Exceptional

cases or particular circumstances may prompt a

reviewing court, where injustice might otherwise

result or where public policy requires, to

consider questions neither pressed nor passed

upon below.

Nuelsen v. Sorensen, 293 F.2d 454, 462 (9th Cir.

1961) (citation and quotations omitted)./2 As we

did in Niedert and Brown, and as the Ninth

Circuit did in Nuelsen, so too have other

circuits acknowledged that they may, when justice

requires it, raise critical issues of law sua

sponte./3 The Ninth Circuit wisely cautioned

that this power must be "exercised sparingly."

Nuelsen, 293 F.2d at 462. This case, however, is

the sort of exceptional case that casts new light

on procedures previously taken for granted.

 If we may sua sponte raise and decide

substantive questions of law, then surely we have

the power to sua sponte alter the procedures we

ask litigants to follow in their efforts to seek

resolution of their substantive questions of law.

It is well settled that stare decisis has less

effect in the context of procedural rules, which

do not serve as a guide to lawful behavior. See

Hohn v. United States, 524 U.S. 236, 251-52

(1998); United States v. Gaudin, 515 U.S. 506,

521 (1995).

 The prosecution of the El Rukn crime

organization has been a deeply troubling episode.

Chief Judge Aspen presided over the first trial

of this particular case, and, in ordering a

retrial, described the situation as tragic,

noting that the prosecutorial misconduct in the

case had wasted years of hard work by the courts,

prosecutors, and law enforcement officers. See

United States v. Boyd, 833 F. Supp. 1277, 1281

(N.D. Ill. 1993), aff’d, 55 F.3d 239 (7th Cir.

1995). Two other El Rukn trials were also

declared mistrials. See United States v. Andrews,

824 F. Supp. 1273 (N.D. Ill. 1993); United States

v. Burnside, 824 F. Supp. 1215 (N.D. Ill. 1993).

As the judiciary was quick to correct an abuse of

power in another branch of government after the

first trial, it also ought to be willing to

correct an error in its own house--even one made

in good faith--so that the public can have

confidence that, even in the most notorious of

criminal cases, the evenhandedness of the

judicial process is above reproach.

 It is time for us to join the rest of the

Country and permit review by appeal of a failure
to recuse under sec. 455(a). I would vacate the

judgments of conviction and order a new trial. 

/1 When a party does not make a fully formed

argument that we should overrule our earlier

precedent to align ourselves with other courts,

the court may consider the argument waived. See

United States v. Martin, 195 F.3d 961, 967 (7th

Cir. 1999). Waiver is not mandatory, of course,

but instead, appellate courts have the discretion

to find that arguments are waived. See, e.g.,

Smith v. Freeman, 892 F.2d 331, 337 n.12 (3d Cir.

1989) (collecting cases). We are therefore under

no obligation to avoid this question.

/2 See also All Care Nursing Serv., Inc. v. Bethesda

Mem. Hosp., 887 F.2d 1535, 1538 n.3 (11th Cir.

1989) (quoting Nuelsen); Boals v. Gray, 775 F.2d

686, 691 (6th Cir. 1985) (same); Cohen v. West

Haven Bd. of Police Comm’rs, 638 F.2d 496, 500

n.6 (2d Cir. 1980) (citing Nuelsen); McKissick v.

United States, 379 F.2d 754, 759 (5th Cir. 1967)

(quoting Nuelsen).

/3 See Curry v. Beatrice Pocahontas Coal Co., 67

F.3d 517, 522 n.8 (4th Cir. 1995) ("The normal

rule of course is that the failure to raise an

issue for review in the prescribed manner

constitutes a waiver. But the rule is not an

absolute one and review may proceed (even

completely sua sponte) when the equities

require." (citation omitted)); Lambert v. Genesee

Hosp., 10 F.3d 46, 56 (2d Cir. 1993) ("However,

we have discretion to consider and decide sua

sponte a dispositive issue of law."); Counts v.

Kissack Water & Oil Serv., Inc., 986 F.2d 1322,

1325-26 (10th Cir. 1993) ("Although it is rarely

done an appellate court may, sua sponte, raise a

dispositive issue of law when the proper

resolution is beyond doubt and the failure to

address the issue would result in a miscarriage

of justice.").