OPINION OF THE COURT
GIBBONS, Chief Judge:
The defendants in several product liability actions pending in the district court petition here pursuant to 28 U.S.C. § 1651 (1982) for a writ of mandamus (1) directing the district judge to vacate an order modifying a discovery order previously entered by a United States magistrate, and (2) reassigning the cases to another judge. Petitioners contend that the challenged order is inconsistent with the mandate of this court in Cipollone v. Liggett Group, Inc., 785 F.2d 1108 (3d Cir.1986), and is otherwise inconsistent with law. They contend, as well, that the district court judge should be removed from the case because of bias against the defendants’ industry. We deny the petition for mandamus and for reassignment.
I.
Prior Proceedings
The Cipollone case is one of eight actions filed on behalf of cigarette smokers in the state and federal courts of New Jersey by the same law firm. There are presently over 100 such cases pending in other jurisdictions. Plaintiffs in all of them are cigarette smokers or their personal representatives who have filed product liability suits asserting negligence, strict liability and intentional wrongdoing by tobacco companies. Claiming that their lung cancer or other smoking-related disease resulted from smoking defendants’ cigarettes, the plaintiffs in those actions allege that the defendants failed to inform consumers adequately of the health risks in smoking and that when health warnings did appear on their products, they were effectively negated by their advertising practices.
This case began in the United States District Court for the District of New Jersey, when Rose Cipollone and her husband, Antonio, filed a complaint on August 1, 1983 against Liggett Group, Inc., Philip Morris, Inc., and Loew’s Theaters, Inc., all of which manufacture cigarettes. Cipollone alleged that as a result of smoking defendants’ cigarettes for almost forty years, she developed bronchogenic carcinoma and sustained other personal injuries. Cipollone sought compensation for her injuries on theories of strict liability and negligence and her husband sought compensation for loss of consortium. Cipollone’s primary contentions were that the defendants had withheld scientific evidence from [337]*337the public and had misrepresented the health hazards of smoking.
A short time later, Susan Haines, administratrix ad prosequendum and executrix of the Estate of Peter F. Rossi brought an almost identical action in the same court against the same defendants as well as R.J. Reynolds Tobacco Co. and the Tobacco Institute, Inc. Haines had the same counsel as Cipollone and sought compensation for Rossi’s pain and suffering and compensation for his death, which allegedly resulted from his smoking defendants’ cigarettes.
Pursuant to 28 U.S.C. § 636 (1982 & Supp. Ill 1985), the district court ordered discovery in both cases under the supervision of then Magistrate Robert E. Cowen. In the fall of 1983, Cipollone made initial discovery requests, of the defendants. The defendants responded by filing motions to strike, claiming that the information sought was irrelevant and that the requests were burdensome and harassing. Magistrate Cowen heard oral argument on those motions on March 22, 1984. A discovery order was issued on May 2, 1984.
Defendant’s counsel then approached Cipollone’s counsel about a confidentiality order. Counsel agreed temporarily not to disseminate any documents “until [they] had an opportunity to attempt to agree upon a Protective Order regarding the documents or, if that [was] not possible [defendants were] to make request for such a Protective Order to the Court.” Letters between counsel dated May 3 and 4, 1984. That agreement was in force until the entry of Magistrate Cowen’s protective order dated March 25, 1985. In the interim, defendants produced thousands of documents and many corporate representatives were deposed. Additionally, discovery of non-parties, including the Tobacco Institute, was conducted. Cipollone’s counsel and the Tobacco Institute’s counsel agreed that if Cipollone wished to disclose confidential material received as a result of that discovery, ten (10) days notice would be given to allow the Tobacco Institute to object. See Letter Agreement dated August 2, 1984. Accordingly, on October 5, 1984, Cipollone’s counsel notified the Tobacco Institute of the intention to disseminate certain confidential documents. See Letter from Marc Z. Edell dated October 5, 1984. Because the Tobacco Institute objected, however, the information was not disseminated.
Meanwhile, negotiations regarding the terms of a protective order broke down because the parties could not agree on Cipollone’s counsel’s right to use the documents obtained in this discovery in other cases, and because of the defendants’ alleged misuse of the “confidential” stamp on documents produced during discovery. On March 25, 1985 Magistrate Cowen entered a protective order for the stated purpose of streamlining the litigation. No specific findings of good cause for the issuance of the protective order were made.
On March 25, 1985, Cipollone appealed the magistrate’s order and the district court, on July 17, 1985, vacated that order and entered a modified order. See Cipollone v. Liggett Group, Inc., 106 F.R.D. 573 (D.N.J.1985). Defendants then petitioned this court for a writ of mandamus, which was granted. See Cipollone v. Liggett Group, Inc., 785 F.2d 1108, 1118 (3d Cir. 1986). Granting the writ, we held that the district court had committed two errors of law: 1) it had applied the wrong standard for issuance of a protective order — first amendment considerations — rather than the less strict “good cause” standard under Fed.R.Civ.P. 26(c); and 2) it had exercised plenary review over the magistrate’s order instead of the review specified in 28 U.S.C. § 636. See Cipollone, 785 F.2d at 1123.
In response to our judgment, Judge Sarokin reconsidered the protective order. He noted that the magistrate had made no specific findings regarding good cause. Judge Sarokin held that the magistrate’s failure to apply a good cause standard was a clear error. See Cipollone v. Liggett Group, Inc., 113 F.R.D. 86, 93 (D.N.J.1986). After considering the defendants’ arguments for finding good cause, the district court rejected them. With regard to the magistrate’s determination of an “umbrella order,” the district court upheld “the aspect of the magistrate’s order that permits defendants to make an initial designa[338]*338tion of confidentiality, subject to their determination that such designation is warranted in good faith, and subject to plaintiff’s later opportunity to challenge such designation and request sanctions pursuant to Fed.R.Civ.P. 26(g).” Cipollone, 113 F.R.D. at 94. Consequently, on December 18, 1986, the district court entered a new modified protective order and issued a supplemental opinion. See Cipollone v. Liggett Group, Inc., Civ. No. 83-2864 (D.N.J. Dec. 18,1986). The magistrate’s protective order remained unchanged except that the district court limited the scope of the order’s protection to “confidential” documents and permitted the use of documents in other related actions.1
[339]*339Defendants then mandamus, claiming petitioned again for that the district court’s order on remand is contrary to law and contrary to this court’s instructions. [340]*340In addition, they request reassignment of this case to another judge, suggesting bias against the defendants on the part of Judge Sarokin.
II.
Scope of Review in Mandamus
In Sporck v. Peil, 759 F.2d 312, 314 (3d Cir.), cert. denied, 474 U.S. 903, 106 S.Ct. 232, 88 L.Ed.2d 230 (1985), we set forth the standards for issuing a writ of mandamus. Two requisites must be found: a) the party seeking the writ must have “no other adequate means to attain the relief he desires,” Allied Chemical Corp. v. Daiflon, Inc., 449 U.S. 33, 35, 101 S.Ct. 188, 190, 66 L.Ed.2d 193 (1980), and b) the trial court must have committed a clear error of law. As we stated in Cipollone, 785 F.2d at 1118, “[mjandamus is not available for abuse of discretion.” The Supreme Court has stated that a writ of mandamus is not readily issued:
Extraordinary writs are “reserved for really extraordinary causes” ..., and then only “to confine an inferior court to a lawful exercise of its prescribed jurisdiction or to compel it to exercise its authority when it is its duty to do so....”
Platt v. Minnesota Mining & Mfg. Co., 376 U.S. 240, 245, 84 S.Ct. 769, 772, 11 L.Ed.2d 674 (1964) (citations omitted). “[T]he moving party [must] satisfy ‘the burden of showing that its right to issuance of the writ is “clear and indisputable” ’.” Will v. Calvert Fire Ins. Co., 437 U.S. 655, 662, 98 S.Ct. 2552, 2557, 57 L.Ed.2d 504 (1978) (citation omitted). The respondents do not dispute that errors with respect to the scope of a protective order probably cannot be corrected by a post-trial appeal. They dispute only whether the second requisite for mandamus has been met — that is, whether the trial court committed a clear error of law.
III.
Discussion
The gravamen of the petitioners’ argument in the instant petition for mandamus is their disagreement with Judge Sarokin’s refusal, on remand, to uphold paragraph 2 of the magistrate’s protective order. Paragraph 2 of the magistrate’s order states that “[a]ll information produced or exchanged in the course of this civil action or any appeal arising therefrom (the “litigation”) shall be used solely for the purpose of this case.” Judge Sarokin, in his protective order of December 18, 1986, replaced that paragraph with paragraphs 2 and 3 which state:
2. All “confidential” information produced by defendants in the course of this civil action or any appeal arising therefrom (the “litigation”) may be used in all related or similar cases subject to the terms and conditions of this order.
3. Any plaintiff seeking to use “confidential or nonconfidential” information from this matter shall seek leave of the court before whom that matter is pending.
{changes italicized).
A. District Court’s Scope of Review Under Section 636
Petitioners’ first argument is that the district court erred again by engaging, on remand, in an impermissible plenary review of the magistrate’s orders rather than applying the “clearly erroneous or contrary to law” standard. Under 28 U.S.C. § 636, a magistrate may hear and determine pretrial matters, which are subject to reconsideration by the district court “where it has been shown that the magistrate’s order is clearly erroneous or contrary to law.” Id. at § 636(b)(1)(A). Petitioners make two contentions to substantiate this argument.
First, petitioners argue that the district court’s “good cause” determinations continued to be based improperly on a concern for the public interest rather than on the interest of the litigants or case management. In support, the petitioners contend that the magistrate’s paragraph 2 imposed no burdens on the respondent and that respondent never complained that the paragraph impeded her ability to go forward [341]*341with her case. The provision, the petitioners argue, merely prevented injury to them and expedited discovery. Citing to a passage in the district court’s opinion, the petitioners insist it proves that the court had a “continuing conception that the public has some legitimate interest in the pretrial disclosure of cigarette company documents.” Petitioners’ Brief at. 17 (emphasis in original).
The district court stated:
... It is inconceivable to this court that under [the] circumstances the public interest is not a vital factor to be considered in determining whether to further conceal that information and whether a court should be a party to that concealment.
However, even ignoring the public interest, defendants have failed to demonstrate any good cause for the concealment of otherwise non-confidential materials from the public in general.
Cipollone, 113 F.R.D. at 87. Petitioners have taken this statement out of context. Judge Sarokin clearly stated that “[t]he Third Circuit has made it clear that first amendment considerations are not implicated in this analysis. It is thus this court’s duty to abide by that mandate.” Id. After that statement, Judge Sarokin went on to express his concern about that ruling, by stating: “However, the court expresses its concern if the public interest is eliminated as a factor in determining whether discovery should be protected from disclosure.” Id. The passage relied on by petitioners followed, and served as an explanation of Judge Sarokin’s concern. Furthermore, there is no indication in the opinion that Judge Sarokin, in making “good cause” determinations, considered the public interest in the documents.
The second contention the petitioners raise in support of their section 636 argument is that, on remand, the district court failed to apply the “clearly erroneous or contrary to law” standard but rather continued to substitute its own judgment for that of the magistrate. The petitioners argue that the district court did not attempt to identify the grounds upon which the magistrate’s general finding of good cause was based. As proof that the district court did not apply the proper standard of review, the petitioners quote from the first district court opinion vacating the magistrate’s order, which stated:
In the usual private litigation not involv- • ing the public interest, it would not be appropriate to permit the release of private materials whose existence and content were disclosed only as the result of the litigation.
Cipollone, 106 F.R.D. at 576. From all of this, the petitioners conclude that “[i]f the district court had in fact abandoned its special public interest test, it could not possibly have found clear error in the entry of the magistrate’s orders.” Petitioners’ Brief at 19 (emphasis in original).
Contrary to the petitioners’ assertions, however, the district court made specific findings that the magistrate’s determination of “good cause” was “clearly erroneous and contrary to law.” The court stated:
In summary, the magistrate’s finding that defendants had shown good cause to support an order that nonconfidential discovery “shall be used solely for the purpose of this case” is clearly erroneous and contrary to law. To the extent that the magistrate found good cause based on embarrassment to defendants, the effect of dissemination on the fairness of trial, or the prior conduct of plaintiffs’ attorney, the finding is clearly erroneous. To the extent that the magistrate found good cause based on a desire to facilitate discovery or to prevent an abuse of the discovery process, the finding is contrary to law.
Cipollone, 113 F.R.D. at 93. In fact, Judge Sarokin correctly noted in his opinion that “[t]he magistrate’s protective order did not contain specific written findings thal good cause existed for prohibiting plaintiffs either from disseminating the fruits of nonconfidential discovery to the public or from utilizing discovery in other litigation.” Id. at 89.
Although Magistrate Cowen mentioned good cause in the March 25,1985 protective [342]*342order, the only stated reason for that order was his desire to streamline the discovery process. See Transcript of Proceedings of March 25, 1985 Before Magistrate Cowen at 56. Thus, it was completely logical for Judge Sarokin not to “attempt to identify the grounds upon which the magistrate’s general finding of good cause was based.” Cipollone, 113 F.R.D. at 89 n. 2. Instead, Judge Sarokin reviewed “the order itself, the transcript of the proceedings before the magistrate and defendants’ briefs and oral arguments,” id. at 89, and found five specific arguments for “good cause” under Rule 26(c). They were that (1) the defendants would suffer financial and other embarassment; (2) fairness at trial would be compromised; (3) the plaintiffs were es-topped from disseminating this material by plaintiffs’ counsel’s prior agreement; (4) discovery in this case would be facilitated; and (5) dissemination would constitute an abuse of the discovery process. The district court then examined the record with respect to each argument and concluded that none of the arguments supported a finding of good cause for an order limiting the use of nonconfidential documents solely to this case. The court specifically ruled that to the extent that the magistrate found good cause based on them, those findings were “clearly erroneous” or “contrary to law.” Cipollone, 113 F.R.D. at 93.
B. Concerns of Case Management
Additionally, petitioners urge that the district court acted inconsistently with this court’s mandate and contrary to law in rejecting the magistrate’s concern about case management as an important basis for the entry of his protective order. That concern appears, however, to have been, not an important basis, but rather the sole basis for the magistrate’s protective order, for in entering it Magistrate Cowen stated:
In the event this decision is appealed or reviewed by higher authority, I want the record to reflect that it’s my opinion, it’s my judgment that having this order in place will facilitate the efficacious production of documents and discovery of the defendants to some extent and that it will streamline the litigation to the point where the discovery sought and had in this case will be for this case and this case alone, and that at the time this case is tried that, of course, anything that goes into the record at that time will be of a public matter and public information.
Transcript of Proceedings of March 25, 1985 Before Magistrate Cowen at 56. No other reason for entry of the order was mentioned. Cipollone argues that the district court did not reject concerns of case management as “a” basis for a protective order but merely rejected it as the sole basis, where the court does not make specific and particularized findings of good cause under Rule 26(c).
Cipollone is correct in this respect. The district court held:
The' magistrate’s reasoning, though based on commendable motives, misconstrues the nature of the “good cause” requirement of Rule 26(c). The magistrate apparently felt that limiting the use of discovery to this case alone would “secure the just, speedy and inexpensive determination” of this action, consistent with the intent expressed in Rule 1 of the Federal Rules. Rule 26(c), however, does not empower individual courts to make such policy decisions. The Rule allows a court to “protect a party or person” — the focus is on injury to a specific individual, not on general concerns of case administration. Rule 26(c), understood as a piece of a larger framework, reflects a policy decision that the “just, speedy and inexpensive” determination of actions is best furthered by permitting the entry of protective orders only to prevent injury to individuals.
The Third Circuit explanation of “good cause” recognizes that the Rule 26(c) inquiry must focus on the harm1 defendants will allegedly suffer from dissemination of discovery material. The Third Circuit directed this court to test defendants’ allegations of harm against the legal standards they provided. Nowhere in the Third Circuit’s directive is this court told that the “good cause” supporting a [343]*343protective order may be general concerns of trial administration.
The magistrate’s rationale that entry of the protective order would facilitate and streamline this litigation is not sufficient “good cause” under Rule 26(c).
Cipollone, 113 F.R.D. at 92-93.
The district court’s summary of the Third Circuit’s mandate in this respect is quite accurate. Judge Becker stated:
... the party seeking the protective order must show good cause by demonstrating a particular need for protection. Broad allegations of harm, unsubstantiated by specific examples or articulated reasoning, do not satisfy the Rule 26(c) test____ Moreover, the harm must be significant, not a mere trifle____
Although there appears to be a lurking dispute as to what may constitute good cause for a protective order, see discussion, supra at pp. 1114-15, we are satisfied that the district court understood and will apply on remand the principle that Rule 26(c) protects parties from embarrassment as well as from disclosure of trade secrets. We add to the district court’s comments only our own understanding that, because release of information not intended by the writer to be for public consumption will almost always have some tendency to embarrass, an applicant for a protective order whose chief concern is embarrassment must demonstrate that the embarrassment will be particularly serious. As embarrassment is usually thought of as a nonmonetizable harm to individuals, it may be especially difficult for a business enterprise, whose primary measure of well-being is presumably monetizable, to argue for a protective order on this ground. Cf Joy v. North, supra [692 F.2d 880 (2nd Cir.1982)] (a protective order will not issue upon the broad allegation that disclosure will result in injury to reputation); to succeed, a business will have to show with some specificity that the embarrassment resulting from dissemination of the information would cause a significant harm to its competitive and financial position.
Cipollone, 785 F.2d at 1121 (citations omitted). Judge Becker clearly focused upon the issue of particular need for party protection, not upon general concerns of trial efficiency. Therefore, the district court’s ruling is not inconsistent with our mandate.
The petitioners further argue, however, that the district court’s rejection of concerns of case management conflicts with our recommendation of the use of umbrella protective orders as “a useful method of dealing with large-scale discovery.” Id. at 1123 (footnote omitted). This is a disingenuous argument and the quote is taken out of context. The quote came at the end of a discussion about an umbrella order approach versus a document-by-document approach to determine confidentiality. See id. at 1122-23. Judge Becker stated:
Under this approach, the umbrella order would initially protect all documents that the producing party designated in good faith as confidential. After the documents delivered under this umbrella order, the opposing party could indicate precisely which documents it believed to be not confidential, and the movant would have the burden of proof in justifying the protective order with respect to those documents. The burden of proof would be at all times on the movant; only the burden of raising the issue with respect to certain documents would shift to the other party.
Id. at 1122 (footnote omitted). In response, the district court abandoned its document-by-document approach and instead adopted in paragraph 4 of its modified protective order, exactly what we advocated.
Perhaps because they are on such unsure ground in relying on claimed inconsistency with our mandate, petitioners next argue that the district court’s holding conflicts with various cases that have recognized that “expedition of discovery and the avoidance of undue burden and expense are sufficient justifications for the entry of protective order provisions like paragraph 2.” Petitioners’ Brief at 22. We question whether, absent inconsistency with our mandate, this contention is appropriately considered in support of a mandamus peti[344]*344tion. Assuming arguendo that it is, the contention is without merit. In support, petitioners string cite five cases which in fact do not stand for such a proposition. In re Consumers Power Co. Securities Litigation, 109 F.R.D. 45 (E.D.Mich.1985), involved a protective order entered by the court on stipulation of the attorneys which was challenged by a non-party newspaper. Applying a first amendment analysis, the court upheld the validity of the order vis-avis the non-party. Chambers Development Co. v. Browning-Ferris Industries, 104 F.R.D. 133 (W.D. Pa.1985), a memorandum opinion outlining the terms of a protective order, merely states that the defendants established good cause under Rule 26(c) but does not discuss how they did so. In re “Agent Orange” Product Liability Litigation, 96 F.R.D. 582 (E.D.N.Y.1983), did not reach the issue of good cause. Rather, a media non-party who had filed a motion to obtain access to non-confidential documents produced by the government was held not to have standing where the party itself had agreed to the order and did not itself assert its right to disseminate discovery documents. In re Korean Airlines Disaster, 597 F.Supp. 621 (D.D.C. 1984), involved the same facts as the Agent Orange case — a consensual protective order which was later challenged by a non-party newspaper — and did not discuss good cause for entry of a protective order. Similarly, Quinter v. Volkswagen of America, 676 F.2d 969 (3d Cir.1982), did not address the issue of good cause but rather involved whether the protective order concerning trade secrets applied to plaintiffs expert witness and whether the witness had violated the order. Thus, Judge Sarokin’s holding is not contrary to any law to which we have been referred. We note also that the district court did not attack the appropriateness of protective orders in general as promoting the efficient management of cases. In fact, Judge Sarokin upheld most provisions of the magistrate’s order. He simply vacated certain of its overbroad provisions.
The petitioners further argue that the district court’s conclusion that courts may not enter protective orders without a specific showing of injury to a specific individual is clear error because 1) it ignores the court’s inherent equitable power over its own process, and 2) it is an overly restrictive reading of Rule 26(c). Citing to International Products Corp. v. Koons, 325 F.2d 403 (2d Cir.1963), in which Judge Friendly held that courts, under their inherent equitable power to control their own process, may enter protective orders against the dissemination of discovery materials, the petitioners urge that, because the district court here did not choose to exercise its inherent equitable power, it committed “clear error.” This argument is without merit. Courts are not required to exercise their inherent equitable powers where there are applicable procedural rules. The district court here complied with the mandate of this court to look for a specific showing of need for protection, while performing a Rule 26(c) analysis. The magistrate did not purport to exercise inherent equitable power.
In addition, petitioners urge that it would be unfair to change the protective order because they relied on it in producing documents up to that point. In support, they cite In re Coordinated Pretrial Proceedings in Western Liquid Asphalt Cases, 18 Fed.R.Serv.2d 1251, 1252 (N.D.Cal.1974), which found that changing a protective order when the parties have relied on it is a “breach of faith,” and to other cases in which courts have refused to vacate protective orders when parties have justifiably relied on them. See, e.g., Martindell v. IT & T Corp., 594 F.2d 291, 296 (2d Cir.1979); GAF Corp. v. Eastman Kodak Co., 415 F.Supp. 129, 132 (S.D.N.Y.1976); Tavoulareas v. Washington Post Co., 111 F.R.D. 653, 658 (D.D.C. 1986); H.L. Hayden Co. v. Siemens Medical Systems, Inc., 106 F.R.D. 551, 555 (S.D.N.Y.1985); Data Digests, Inc. v. Standard & Poor’s Corp., 57 F.R.D. 42 (S.D.N.Y.1972).
While this argument at first blush has appeal, these cases are persuasive only if, in producing documents, the petitioners justifiably relied on the protective order. As Cipollone correctly points out, however, hundreds of thousands of documents were [345]*345produced in the instant case before the magistrate’s protective order of March 25, 1985. After a long discovery dispute, on May 2, 1984, Magistrate Cowen issued a discovery order allowing plaintiffs narrow discovery. So far as the record discloses, prior to that no discussions or negotiations had taken place regarding a protective order. Subsequently, petitioners approached Cipollone about a protective order. Cipollone agreed that truly confidential documents should not be disclosed but never agreed to a broad sweeping umbrella protective order including non-confidential documents or to limiting the use of the documents in other cases. Apparently, Cipollone agreed temporarily not to disseminate any documents “until [they] had an opportunity to attempt to agree upon a Protective Order regarding the documents or, if that [was] not possible to make a request for such a Protective Order to the Court.” Letters between counsel dated May 3 and 4, 1984. Thus, reliance cannot be justifiably based on this interim agreement. Further, once the protective order was issued over Cipollone’s objection, an appeal by Cipollone was filed within 10 days. See Notice of Motion to Vacate Magistrate’s Protective Order filed April 4,1985. Clearly respondent never agreed with the protective order and no order was in place when most of the documents were produced. Thus, reliance under these facts cannot fairly be found, and was properly rejected.
Finally, petitioners quarrel with Judge Sarokin’s application of Rule 1, maintaining that he inconsistently applied the rule in two different parts of his opinion. Again, petitioners’ argument is without merit. The district court observed that the Rule 1 consideration that federal rules “be construed to secure the just, speedy and inexpensive determination of every action.” Fed.R.Civ.P. 1, militates against limiting the use of discovery material in other litigation. See Cipollone, 113 F.R.D. at 91. Later in the opinion, Judge Sarokin ruled that the magistrate’s limitation on the use of documents, apparently pursuant to Rule 1, was inconsistent with the good cause requirement of Fed.R.Civ.P. 26(c). He reasoned that “Rule 26(c), understood as a piece of a larger framework, reflects a policy decision that the ‘just, speedy and inexpensive’ determination of actions is best furthered by permitting the entry of protective orders only to prevent injury to individuals.” Cipollone, 113 F.R.D. at 92-93. There is nothing inconsistent in the court’s analysis.
C. Evidence of Potential Financial Harm
The petitioners contend that the district court erred in concluding that their submissions on potential financial harm were inadequate. They believe that the magistrate’s protective order should have been upheld on this basis. This court, in issuing our writ of mandamus, instructed the district court that to show good cause “a business will have to show with some specificity that the embarrassment resulting from dissemination of the information would cause a significant harm to its competitive and financial position.” Cipollone, 785 F.2d at 1121. We also stated that “[b]road allegations of harm, unsubstantiated by specific examples or articulated reasoning, do not satisfy the Rule 26(c) test.” Cipollone, 785 F.2d at 1121.
According to the petitioners, they submitted the following proofs:
(1) that counsel for plaintiffs intended to disseminate to the general public selected portions of the material received by them in discovery;
(2) that counsel for plaintiffs intended to accompany such dissemination with slanted “explanations” of the significance of particular documents;
(3) that counsel for plaintiffs have regularly attended and participated in symposia and seminars concerning the smoking and health litigation, including those sponsored by securities analysts;
(4) that securities analysts closely follow the smoking and health litigation, and have rendered opinions and issued investment advice, including a decision to downgrade their investment opinions concerning tobacco stocks such as those of defendants Reynolds and Philip Morris, based directly upon developments in this litigation;
(5) that major institutional investors in tobacco stocks independently monitor [346]*346such developments and make decisions to invest in or disinvest of tobacco stocks, including stocks of defendant R.J. Reynolds, based upon these developments;
(6) that the market in tobacco company stocks has been sensitive to developments in this litigation;
(7) a market analysis distributed by the investment firm of Drexel Burnham Lambert which referred to the “obvious volatility” of tobacco stocks in relation to events arising out of the smoking and health litigation;
(8) evidence that the firm of E.F. Hutton has noted that the viability of tobacco stocks was “directly related” to product liability litigation.
Petitioners contend that Judge Sarokin mischaracterized and ignored their submissions. He did not. Rather, he made a careful analysis of petitioners’ submissions concerning potential financial harm. See Cipollone, 113 F.R.D. at 89-91. He considered the contention that the market price of defendants’ stock will be adversely affected but found that “[s]uch a sweeping allegation” does not rise to the level of specificity required by Rule 26(c). See Cipollone, 113 F.R.D. at 90. Noting the “only specific ‘example’ cited by defendants” — “that Philip Morris stock increased in value ten points after the Third Circuit’s issuance of their writ of mandamus” — the court found that the petitioners here, unlike the petitioners in Tavoulareas,2 never specifically demonstrated how dissemination would hurt their business. See Cipollone, 113 F.R.D. at 90. Failing to provide the district court with a single document as a concrete example of the type of harm they would suffer, petitioners made only broad allegations of harm. Although the petitioners claim that “[t]he district court's opinion indicates that nothing will do but a showing, document-by-document and deposition-by-deposition, that each, separately released, would in fact cause a fall in the market for defendants’ securities,” Petitioners’ Brief at 31, there is nothing in the opinion which substantiates such a proposition. The district court stated:
Defendants have shown that their financial standing has been affected by this and related litigation. Defendants have not substantiated, however, how preventing the release of all discovery materials is needed to prevent particularized, significant injury to their financial and competitive position. Defendants have not identified a single document which they contend will or might have such an effect.
Id. Obviously, the district court did not require a document-by-document showing. It was merely looking for concrete examples.3
IV.
Remand to a Magistrate
We note that the petitioners did not assert in the district court, or in the petition here, that our mandate required the district court to do anything more than reconsider the previous ruling in light of the two legal errors which this court found. Indeed, the district court undertook exactly such a reconsideration and so it is not surprising that the petitioners have not urged either a new hearing or new factfinding. We find no basis, therefore, in the petition or in the representations made by petitioners for considering a contention that the district court should have permitted either the creation of a new record or a new opportunity for factfinding by a different magistrate.
[347]*347V.
Reassignment
Petitioners contend that the case should be reassigned to a different judge because of Judge Sarokin’s bias, which, they insist, is demonstrated because: 1) he did not follow our prior mandate; 2) his rulings indicate hostility to the tobacco industry; and 3) he has prejudged critical factual disputes. Each of these bases for suggesting bias lacks merit.
As we conclude in Part III above, Judge Sarokin did follow our mandate. Additionally, even if he had not, that alone, despite the petitioners’ insistence to the contrary, is not a sufficient basis to remand to a different district court judge. It does not establish bias. In this area, we may take instruction from cases arising under 28 U.S.C. § 144 (1982), and its predecessor, section 21 of the Judicial Code (1911), ch. 231, § 21, 36 Stat. 1087, 1090 (1911). See Berger v. United States, 255 U.S. 22, 31, 41 S.Ct. 230, 232, 65 L.Ed. 481 (1921) (“bias or prejudice which can be urged against a judge must be based upon something other than rulings in the case” and the disqualification statute “was never intended ... to enable a .discontented litigant to oust a judge because of adverse rulings”); accord Hanger v. United States, 398 F.2d 91, 101 (8th Cir.1968), cert. denied, 393 U.S. 1119, 89 S.Ct. 995, 22 L.Ed.2d 124 (1969).
In support of their contention that Judge Sarokin’s ruling demonstrates hostility to the tobacco industry, petitioners point to the district court’s first decision on the protective order, in which the court entered an order requiring petitioners to file briefs with the magistrate to justify the claim of confidentiality for each document so designated. This, they correctly state, was more relief than Cipollone requested. That order, however, has been rescinded and the district court’s modified protective order is in compliance with our mandate. An error of law, corrected by a reviewing court, does not establish bias.
Finally, the petitioners accuse Judge Sarokin of prejudging critical fact issues that have not been yet heard. These issues are: “(1) whether consumers have been adequately informed of the dangers of smoking; (2) whether smokers are properly viewed as ‘victims’ of their smoking; and (3) whether cigarettes are addicting.” Petitioners’ Brief at 46-47. In support, petitioners quote various sentences in 649 F.Supp. 664 (D.N.J.1986), 593 F.Supp. 1146 (D.N.J. 1984) and slip op. (D.N.J. Dec. 7, 1984), which, they say, show that the district court has already decided these issues. See Petitioners’ Brief at 47-56. All are taken out of context and exaggerated. They are not worth setting forth here.
The petition that we remove Judge Sarokin from the case by exercising our authority under 28 U.S.C. § 1651 to protect petitioners from bias is entirely without merit, and a thinly disguised effort at judge shopping.
VI.
Conclusion
The district court on remand following the previous decision in this case complied in good faith with our mandate. The court committed no clear error of law in modifying the magistrate’s protective order. The petitioners’ suggestion of bias is entirely without merit. The petition for mandamus will therefore be denied.