OPINION

In an effort to hasten resolution of the Federated Department Stores’ and other debtors’ bankruptcy estate, the Bankruptcy Court for the Southern District of Ohio ordered those creditors who had litigation pending against the debtors to submit their claims to non-binding arbitration before bringing their claims to court. Creditors were given an opportunity to opt out of this dispute resolution process, and some did. Appellants Christopher and Marion Spierer, however, did not, and the bankruptcy court stayed their state court suit against the debtors until the Spierers had gone through the arbitration process. The Spierers subsequently sought to lift the stay so that they could proceed directly in state court, however, arguing that the stay should never have been imposed. The bankruptcy court denied this motion, and the district court affirmed on the grounds that the Spierers could not challenge the imposition of the stay in their appeal from the denial of a motion to lift the stay. To the extent that the Spierers challenge the bankruptcy court’s jurisdiction to impose.the stay, we may hear the appeal. Because the stay was within the bankruptcy court’s jurisdiction, however, we AFFIRM the judgment of the bankruptcy court.

I. BACKGROUND

Claiming that they had suffered injuries as a result of exposure to toxic chemicals in a mattress that they had obtained from the defendants, Christopher and Marion Spierer filed suit against the Federated Department Stores and certain of Federated’s subsidiary companies in New York state court in 1987. The Spierers were not the only individuals who were suing the defendants, and on January 15, 1990, the defendants — now the Debtors — filed for bankruptcy protection in the U.S. District Court for the Southern District of Ohio. Later that year, having determined that no global settlement of the claims against the Debtors was imminent, the bankruptcy court lifted the automatic stay on all pending litigation. The Spierers were then free to proceed with their claim and apparently began preparing for a trial in New York state court.

Of the thousands of claims that had been brought against the Debtors, all but a few were resolved over the next several years, and in the interest of settling the estate quickly, the Debtors had moved the bankruptcy court to adopt an Alternative Dispute Resolution (“ADR”) procedure for any remaining claims. With all parties in interest having been given notice and after *832holding a hearing, the bankruptcy court agreed to order the remaining claimants, including the Spierers, to bring their claims first tó ADR. On January 8, 1997, the bankruptcy court stayed all litigation over personal injury claims then pending against the Debtors. In doing so, the bankruptcy court cited as authority sections 105, 524, and 1141 'of Title 11. Section 105 grants bankruptcy courts the power to issue “any order ... necessary or appropriate” to accomplish the bankruptcy code’s provisions. 11 U.S.C. § 105. Section 1141 provides that the confirmation of a reorganization plan vests all of the estate’s property in the hands of the debtor, see 11 U.S.C. § 1141(b), and section 524(a) states that a discharge in bankruptcy serves as an injunction against actions to collect on the debtor’s personal liabilities, see 11 U.S.C. § 524(a).

At least one claimant who had objected to the Debtors’ ADR proposal was exempted from the ADR process so long as his trial would be commenced by a certain date, but claimants such as the Spierers who had not opposed the proposal were required to submit their claims to arbitration. Claimants could choose whether the arbitration would be binding, and if claimants bringing personal injury actions chose for the arbitration to be non-binding, they could serve notice within ten days of the non-binding decision that they still intended to litigate their claims.

Although the Spierers had not opposed the mandatory ADR procedure before it was adopted, they soon let their feelings on it be known. Having moved to Florida, the Spierers claimed that a medical condition prevented them from traveling to New York for the arbitration. In 1999, the bankruptcy court denied the Spierers’ request that the arbitration be ordered to occur in Boca Raton, Florida, as the bankruptcy court determined that the choice of venue for the ADR would best be left to the arbitrator. The bankruptcy court also denied their request that they be exempted from the ADR process altogether and be permitted to litigate without first going through the ADR. Finally, the bankruptcy court made clear that matters governing discovery in the ADR process would be left to the arbitrator. The Spierers filed no notice of appeal from these orders.

The Spierers still objected to the ADR process, however, and moved the bankruptcy court to lift its stay on litigation. In the May 18, 2001 order from which the Spierers now appeal, the bankruptcy court noted that the Spierers had missed their opportunity to opt out of the ADR process and that the ADR would expedite the settlement of the remaining claims. Accordingly, the bankruptcy court refused to lift its prior stay on litigation, and it held that the Spierers were bound to use the ADR process before they could go to court.

The Spierers filed a notice of appeal frqm that May 18, 2001 order and brought their claim to the district court, which had jurisdiction over the interlocutory appeal pursuant to 28 U.S.C. § 158(a)(3). As they do before this court, the Spierers argued that the bankruptcy court had lacked the power to send their claims to ADR. The district court ruled that this attack was on the January 8, 1997 order imposing the ADR plan, and that the January 8, 1997 order could not be challenged in an appeal from the May 18, 2001 refusal to lift the stay. The district court thus dismissed the appeal.

The Spierers timely appealed to this court, and we have jurisdiction over final orders of the district court under 28 U.S.C. § 158(d). We review the decision of the bankruptcy court directly, reviewing its factual findings for clear error and its legal conclusions de novo. Harker v. Troutman (In re Troutman Enterprises, Inc.), 286 F.3d 359, 363 (6th Cir. 2002).

*833II. ANALYSIS

A. Appellate Jurisdiction

Although the Spierers’ Notice of Appeal to the district court explicitly stated that they were appealing from the bankruptcy court’s May 18, 2001 order denying their Motion to Lift the Stay, and made no mention of the January 8, 1997 order that imposed the stay, the Notice is sufficient to allow them to challenge the bankruptcy court’s jurisdiction to impose the stay. To be sure, the May 18, 2001 order was not a final judgment, an appeal from which would necessarily incorporate “ ‘all prior non-final rulings and orders.’ ” Newman v. Fed. Express Corp., 266 F.3d 401, 404 (6th Cir. 2001) (quoting Crawford v. Roane, 53 F.3d 750, 752 (6th Cir. 1995), cert. denied, 517 U.S. 1121, 116 S.Ct. 1354, 134 L.Ed.2d 522 (1996)). And indeed, we construe a notice of appeal from a particular interlocutory order as being limited to that order. See Crawford, 53 F.3d at 752. Here, however, by appealing from the court’s refusal to lift the stay, the appellants necessarily called into question the court’s jurisdiction to impose it. It goes without saying that if the bankruptcy court lacked the power to impose the stay in the first place, then the Motion to Lift the Stay should have been granted. Although it does not appear that the bankruptcy court’s jurisdiction to have issued the stay was discussed in the order from which the appeal was taken, courts “review[ ] judgments, not opinions” or arguments, see, e.g., Chevron U.S.A. Inc. v. Natural Res. Def. Council, Inc., 467 U.S. 837, 842, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984), so the appellate court reviewing the judgment refusing to lift the stay must consider whether the law required otherwise.

Of course, the Spierers have waived most of the arguments that might support the theory that the stay was improperly imposed. Their Motion to Lift the Stay never suggests, for example, that the stay exceeded the bankruptcy court’s statutory power under 11 U.S.C. §§ 105, 524, or 1141. Accordingly, the Spierers have waived the argument that imposing the stay violated the statutory restrictions. See Overstreet v. Lexington-Fayette Urban County Gov’t, 305 F.3d 566, 578 (6th Cir. 2002).

However, the Spierers could not have waived the argument that the January 8, 1997 order imposing the stay exceeded the bankruptcy court’s subject matter jurisdiction. “[I]t is hornbook law that parties may not waive into or consent to subject matter jurisdiction which a federal court does not properly have.” Universal Consol. Cos. v. Bank of China, 35 F.3d 243, 247 (6th Cir. 1994). That the Spierers failed to suggest while before the bankruptcy court that the stay was imposed in violation of Article III is irrelevant, as “subject-matter jurisdiction can be challenged at any time.” Taubman Co. v. Webfeats, 319 F.3d 770, 773 (6th Cir. 2003) (noting that subject matter jurisdiction can even be raised collaterally pursuant to Fed.R.Civ.P. 60(b)(4)).

The Supreme Court’s practice in Mitchell v. Maurer, 293 U.S. 237, 55 S.Ct. 162, 79 L.Ed. 338 (1934), supports our approach here. In Mitchell, a party from Delaware sought in a California federal court to have certain property located in California but owned by a Delaware corporation placed in receivership. Id. at 238-39, 55 S.Ct. 162. The district court appointed a receiver, and later, California state officials moved to vacate the appointment, arguing unsuccessfully that state officials had taken possession of the property before the request for the receiver had been filed in federal court. See id. at 239-40, 55 S.Ct. 162. The Supreme Court refused to address the parties’ arguments regarding whether the state officials had properly taken possession of the property, id. at 241-42, 55 S.Ct. *834162, and instead ruled that because the original parties were not sufficiently diverse, the district court had lacked subject matter jurisdiction to appoint the receiver in the first place, see id. at 242-44, 55 S.Ct. 162. Having determined that the court had lacked jurisdiction to issue the original order, the Supreme Court ordered the district court to dismiss the case altogether. Id. at 244, 55 S.Ct. 162. Just as the Supreme Court could address there whether the lower court had jurisdiction to issue the original order, even when it was the management of that order and not the issuance of it that was on appeal, we have jurisdiction to address whether the lower court had jurisdiction to impose a stay even though it is the refusal to lift the stay, not its issuance, that is on appeal. The jurisdictional question could not have been waived.1

Thus we have jurisdiction over the Spi-erers’ claims to the extent that they mount a jurisdictional challenge to the January 8, 1997 order imposing the stay. We address only the Spierers’ argument that the stay violates jurisdictional limits, and we make no statement on whether the stay was an abuse of discretion or other non-jurisdictional arguments. The Spierers waived those arguments by not presenting them to the bankruptcy court when they moved it to lift the stay. The Spierers also may not challenge the bankruptcy court’s order of September 22, 1997, in which it refused to settle disputes over venue and discovery in the ADR process, because although the Spierers cast their objections to those orders in terms of the bankruptcy court having stripped itself of jurisdiction, those claims are in no way incorporated in the Notice of Appeal from the May 18, 2001 order. That is, the decision on the Motion to Lift the Stay on pending state court litigation does not require any judgment as to whether the ADR process treated discovery and venue issues appropriately.

B. Merits of the Appeal

Whether or not the plaintiffs could meet the high burden of showing that the bankruptcy court abused its discretion in staying the state court litigation under 11 U.S.C. § 105(a), there is no doubt that the statute gives bankruptcy courts jurisdiction to do so. See, e.g., id. § 105(a) (“The court may issue any order, process, or judgment that is necessary or appropriate to carry out the provisions of this title.”). Accordingly, the jurisdictional challenge to the January 8, 1997 order imposing the stay and requiring the parties to go to ADR before litigating is purely a constitutional question governed by the line of cases beginning with Northern Pipeline Construction Co. v. Marathon Pipe Line Co., 458 U.S. 50, 102 S.Ct. 2858, 73 L.Ed.2d 598 (1982).2

*835In Northern Pipeline, the Supreme Court struck down a provision of the 1978 Bankruptcy Act that gave bankruptcy judges full power to issue final orders and judgments in eases that were only “related to” Title 11 cases. A plurality reasoned that although Congress could empower non-Article III judges to issue final orders and judgments in cases involving bankruptcy . rights, because those rights existed only because of a congressional grant, Congress could not empower non-Article III judges to act with the full “judicial Power of the United States,” U.S. Const, art. Ill, § 1, in cases involving rights that, like the right to recover under state law for a personal injury at issue here, existed independent of any congressional grant. Accordingly, the plurality ruled that the bankruptcy court could not issue a final judgment in a state law contract case brought by a debtor.3 See Northern Pipeline, 458 U.S. at 63-87, 102 S.Ct. 2858. In Commodity Futures Trading Commission v. Schor, 478 U.S. 833, 106 S.Ct. 3245, 92 L.Ed.2d 675 (1986), the Court endorsed a case-by-case, functional inquiry into Article III challenges:

Among the factors upon which we have focused are the extent to which the “essential attributes of judicial power” are reserved to Article III courts, and conversely, the extent to which the non-Article III forum exercises the range of jurisdiction and powers normally vested only in Article III courts, the origins and importance of the right to be adjudicated, and the concerns that drove Congress to depart from the requirements of Article III.

Id. at 851, 106 S.Ct. 3245. No one factor predominates. Id.

Crucial here is that a bankruptcy court’s power to stay other litigation leaves the essential attributes of the nation’s “judicial Power,” U.S. Const, art. Ill, § 1, safely in the Article III courts. The federal district court maintains all of its previous powers. Granting the bankruptcy court this ability to stay state court proceedings in no way aggrandizes Congress’s power with respect to the judiciary, see Schor, 478 U.S. at 850, 106 S.Ct. 3245, as Article III tribunals maintain oversight of the bankruptcy court’s action. The fact that ultimate review of the non-Article III tribunal’s actions rests in Article III courts indicates that the Article III courts retain an unquestionably important aspect of their judicial power. See Norris v. Schotten, 146 F.3d 314, 325-26 (6th Cir.) (emphasizing importance of Article III review of federal magistrate judges’ decisions), cert. denied, 525 U.S. 935, 119 S.Ct. 348, 142 L.Ed.2d 287 (1998); Richard H. Fallon, Jr., Of Legislative Courts, Administrative Agencies, and Article III, 101 Harv. L.Rev. 915, 950-74 (1988) (suggesting that review by Article III court is *836necessary and sufficient condition of reserving appropriate power in Article III courts).

Second, the power exercis.ed by the bankruptcy court is not one that must be exercised exclusively within the confines of Article III. The order enjoining the state proceedings pending non-binding arbitration does not resolve that litigation, but merely affects its timing. This power to impose a stay is thus far from the “ultimate decisionmaking authority,” Northern Pipeline, 458 U.S. at 79, 102 S.Ct. 2858, that must remain in the Article III court. Rather, it is one of the many “functions historically performed by judges,” id. at 80, 102 S.Ct. 2858, that may be statutorily delegated to non-Article III judges. Congress can, after all, order certain parties to submit to arbitration with limited Article III review without encroaching on the realm of Article III, see Thomas v. Union Carbide Agric. Prods. Co., 473 U.S. 568, 105 S.Ct. 3325, 87 L.Ed.2d 409 (1985) (upholding statute that required applicants for EPÁ pesticide permits who cannot agree on how to share costs of certain research to submit to arbitration with only minimal Article III review), which suggests that the power to stay 'proceedings pending non-binding arbitration is not a power exclusive to Article III. Cf. First Fed. Sav. Bank & Trust v. Ryan, 927 F.2d 1345, 1359 (6th Cir.) (“[T]he appointment of a conservator or receiver is not a 'judicial power’ subject to Article III.”), cert. denied, 502 U.S. 864, 112 S.Ct. 187, 116 L.Ed.2d 148 (1991); Noriega-Perez v. United States, 179 F.3d 1166, 1175-76 (9th Cir. 1999) (finding that although ALJ’s imposition of a fine “may seem to be within the purview of an Article III court, this concern is mitigated because ALJs do not have the authority to enforce the fine”); In re Clay, 35 F.3d 190, 193 (5th Cir. 1994) (calling the power to conduct jury trials “the heart of ‘the judicial Power’ ”).

With respect to Schor’s third and fourth criteria, although the right at issue is an important one, the restrictions imposed on that right are minimal and for important and legitimate purposes. Whereas Congress’s power to relegate cases involving “public” rights to non-Article III fora is unquestioned, see Granfinanciera, S.A. v. Nordberg, 492 U.S. 33, 50-54, 109 S.Ct. 2782, 106 L.Ed.2d 26 (1989), we should be wary of limiting the ability to enforce rights that exist between private parties and independently of any congressional action, see Northern Pipeline, 458 U.S. at 83-84, 102 S.Ct. 2858 (plurality); id. at 91, 102 S.Ct. 2858 (Rehnquist, J., concurring). As suggested above, however, the restriction at issue here is minimal, as it affects not the ability to enforce these private rights, but only the timing of that enforcement. Granting bankruptcy courts this power protects the court’s ability to administer the estate efficiently and other creditors’ ability to satisfy their claims.

We thus conclude that the power to stay other pending litigation involving the debtors or the estate is within the bankruptcy court’s constitutional jurisdiction.

Finally, to whatever extent the Spierers wish to challenge the denial of their Motion to Lift the Stay on the grounds that, even if the stay had been imposed pursuant to the bankruptcy court’s proper powers, the stay should have been lifted in the May 18, 2001 order, their challenge fails. We review a bankruptcy court’s refusal to lift a stay for abuse of discretion. See White v. White (In re White), 851 F.2d 170, 174 (6th Cir. 1988). The refusal to lift the stay appears to have been well within the bankruptcy court’s discretion. The bankruptcy court noted that the earlier January 8, 1997 order, which required certain remaining claimants to bring their claims in ADR before litigating, had aimed to “expedit[e] *837the resolution of a relatively few remaining claims.” J.A. at 410. Although the Spier-ers claim that this ADR process imposed an unnecessary hardship on them, arguing that their health would prohibit them from traveling to New York for the hearing and that the arbitrator’s proposed alternative of a videoconference was prohibitively expensive, the bankruptcy court did not abuse its discretion in finding that ADR’s expeditious procedures outweighed the Spierers’ hardships: The Spierers had counsel in New York who presumably could have represented their interests at the ADR, their proposed alternative of litigating in New York state court appears to impose no less of a burden, and under the January 8, 1997 order’s ADR plan, the Spierers could still proceed to court even if they participated in the ADR and lost. Further, as the bankruptcy court noted, at least one other claimant objected to the ADR proposal and was exempted from the process so long as he proceeded in state court in a timely manner; this route appears to have been equally open to the Spierers.

III. CONCLUSION

Because we determine that we have jurisdiction to consider the Spierers’ Article III challenge to the January 8, 1997 order, we VACATE the district court’s judgment dismissing the appeal. Because the order refusing to lift the stay was within the bankruptcy court’s jurisdiction, however, we AFFIRM the judgment of the bankruptcy court.