A confirmed plan of reorganization provided that certain claims against the Chapter 11 debtor and its non-debtor affiliates would be resolved in a court of competent jurisdiction and determined by settlement or final judgment. The debtor, its affiliates, and the claimants later requested the bankruptcy court’s approval of a proposed agreement to liquidate the claims through binding arbitration. The bankruptcy court denied the request, and the district court affirmed that judgment. This appeal presents a subject matter jurisdiction challenge and the substantive issue of whether the proposed agreement constitutes an impermissible attempt to modify a substantially consummated plan of reorganization. We find that the bankruptcy court had jurisdiction over this matter and agree with its determination that the proposed agreement would modify the plan in violation of the Bankruptcy Code. Accordingly, we AFFIRM.

I. BACKGROUND

Between 1975 and 1990, United States Brass Corporation manufactured and marketed a polybutylene plumbing system for residential and commercial construction, repair, and remodeling. U.S. Brass produced the pipe and fittings used in the plumbing system from raw materials supplied by Shell Oil Company and CNA Holdings, Inc. (formerly Hoechst Celanese Corporation). The system turned out to be defective, and, as a consequence, numerous homeowners, homeowners associations, developers, builders, and plumbing contractors sued U.S. Brass, U.S. Brass’s parent corporations,1 Shell, and CNA (col*300lectively “the Appellants”)- According to U.S. Brass, its insurers’ unwillingness to defend or provide coverage for the lawsuits caused the company to file for bankruptcy protection in the Eastern District of Texas on May 23,1994.

Shell and CNA filed a joint claim in the U.S. Brass Chapter 11 case for $1,012,732,856.00, representing the companies’ actual and estimated expenditures in connection with the defective plumbing system and the resulting litigation. Shell also filed a separate proof of claim in the amount of $53,331,738.00 for funds it expended in settlement of homeowners’ claims involving U.S. Brass products.

Resolving the Shell/CNA plumbing claims was a principal object in drafting a plan of reorganization for U.S. Brass. And it became clear early in the drafting process that the debtor and its affiliates were relying heavily on insurance proceeds to satisfy those claims. Consequently, the Appellees (“Insurers”), who issued insurance policies to U.S. Brass and Eljer covering the period of the plumbing system’s manufacture and installation in buildings throughout the country, were active in the reorganization. In particular, the Insurers objected to the September 24, 1997 version of the reorganization plan because they feared it would invite collusive behavior among the debtor, Eljer, Shell, and CNA in the liquidation of the Shell/CNA claims. The.Insurers were also concerned that the proposed plan would prevent them from asserting coverage defenses arising from violations of the “cooperation” and “no action” provisions of their policies. According to the Insurers, those provisions require U.S. Brass and Eljer to cooperate with them in defending plumbing claims and relieve the Insurers of their indemnity obligations unless the claims are fully and fairly adjudicated or settled with the Insurers’ approval.

The Insurers eventually withdrew their objections to confirmation, but only after the plan was amended to preserve their coverage defenses for later adjudication in ongoing coverage litigation.2 Through the amendment, the parties also formalized a method for resolving the Shell/CNA claims by adding plan sections 8.20(b) and 8.21. Section 8.20(b) requires that the claims be asserted “by institution of litigation in a court of competent jurisdiction,” with recovery to be “determined by settlement or final judgment”; section 8.21 sets forth a time limit for such litigation to be commenced or continued.3

*301Even before the amendment, however, the parties understood that the Shell/CNA claims would be litigated. Both the September 1997 and final versions of the plan included section 4.1(e)®, which mandates an alternative dispute resolution procedure for the liquidation of other outstanding plumbing claims, primarily those of homeowners. That procedure permits binding arbitration proceedings if agreed to by the parties. But section 4.1(e)(iv) exempts the Shell/CNA claims from the ADR mechanism.4 Thus, the ADR provisions do not conflict with or undermine the later-added litigation requirement for the Shell/CNA claims.

The bankruptcy court confirmed the amended plan on February 24, 1998, and incorporated into its Confirmation Order the Stipulation Between the Debtor and Certain Named Insurers. The stipulation provided that U.S. Brass and Eljer would defend the Shell/CNA claims in good faith and not seek to end that litigation through collusive trial or settlement with the claimants.

On March 19, 1998, the plan became effective, and, as prescribed by its initial funding provisions, U.S. Brass and Eljer made a cash payment to the Brass Trust, the entity created to receive and distribute funds to plumbing claimants and other creditors. Pursuant to a settlement agreement included in the plan, Shell and CNA received $2,500,000.00 on their claims. The plan provides that the remainder of the Shell/CNA claims, still exceeding one billion dollars in the companies’ estimate, could be recovered only from insurance proceeds. Furthermore, the plan requires any proceeds recovered on the Shell/CNA claims to be paid over to the Brass Trust. Eighty percent of those proceeds would then be distributed to the claimants in the Cox class action,5 thereby reducing Shell *302and CNA’s payment obligations to the class.6 The remaining twenty percent would be available for other plumbing claimants.

In accordance with the plan, Shell and CNA instituted litigation against Eljer in the courts of New Jersey and filed suit against U.S. Brass in Collin County, Texas. On March 12, 1999, this court dismissed as moot an appeal from the bankruptcy court’s Confirmation Order.7 We found that “the transactions that have taken place to date, the exchange of mutual releases, the disbursements already made, and the general implementation of the plan by all the involved parties evidence substantial consummation of the plan.”8

On October 18,1999, the Appellants filed a “Motion for Order in Aid of Consummation of Plan and for Approval of Settlement of Plumbing Claims of Shell Oil Company and Hoechst Celanese Corporation” with the bankruptcy court. The motion requested the court’s approval of a proposed settlement agreement among U.S. Brass, Eljer, Shell, and CNA. Under the agreement, the Shell/CNA claims would be liquidated by submission to final and binding arbitration. In addition, the pending lawsuits in New Jersey and Texas would be dismissed, but the limitations period of plan section 8.21 would be tolled so that those suits could be reinstituted if necessary.

The Insurers filed objections to the motion, contending that arbitration of the claims without their consent would alter their rights under the plan and constitute a breach of the “cooperation” and “no action” clauses of the U.S. Brass/Eljer polices. After a full evidentiary hearing, the bankruptcy court denied the motion on two bases. First, the court found that the proposed agreement “fails to settle any matter before the courts”:

[T]he testimony offered at the hearing on the Motion made it abundantly clear to this Court that the proposed agreement will not end, expedite or curtail litigation of the Shell/[CNA] claims. It is no settlement at all. No arms length bargaining has occurred. No value has changed hands. No claims have been released or reduced. The Motion simply seeks to substitute an arbitration process for the resolution of those claims which the confirmed Plan required to be litigated in a court of competent jurisdiction and determined by settlement or final judgment.9

*303Second, the court recognized that 11 U.S.C. § 1127(b) “prohibits modification of a substantially consummated plan of reorganization” and concluded that approving the Appellants’ motion would violate this prohibition:

The proposed “settlement” agreement alters by extension the provisions of the Plan respecting time limitations with respect to bringing actions if the arbitration results in giving the carriers a defense to coverage. Plan at 8.21. Moreover, arbitration (as to the claims which are the subject matter of the proposed “settlement”) was not an option specifically contemplated and negotiated by the parties at confirmation. The Court will not and may not allow such a modification of a confirmed and substantially consummated plan of reorganization in contravention of 11 U.S.C. § 1127(b) regardless of Movants’ attempts to clothe it as a settlement or clarification of an order.10

U.S. Brass, Eljer, Shell, and CNA appealed the bankruptcy court’s order denying the motion to the United States District Court for the Eastern District of Texas. The district court affirmed, finding that the Appellants’ proposed substitution of arbitration for litigation in a court of competent jurisdiction “should not be interpreted as a ‘settlement’ because the carefully crafted claims resolution scheme set forth in the Plan does not contemplate arbitration. If the parties had intended to resolve the Shell/CNA claims through arbitration, they would have specifically provided for arbitration in the Plan language.” Thus, the district court agreed that “the Motion is appropriately viewed as an attempt to ‘modify’ the Plan in violation of 11 U.S.C. § 1127(b).”

The Appellants now seek review in this court.

II. JURISDICTION

Citing the limited nature of post-confirmation jurisdiction, the Insurers contend that the bankruptcy court lacked authority to entertain the Appellants’ motion. “Both the bankruptcy and district courts’ finding that they had subject matter jurisdiction is a legal determination that we review de novo.” 11 In asserting jurisdiction, the bankruptcy court relied on both a broad retention-of-jurisdiction provision in the confirmed plan and its authority under the Bankruptcy Code to clarify and enforce its own orders.12 “However, the source of the bankruptcy court’s subject matter jurisdiction is neither the Bankruptcy Code nor the express terms of the Plan. The source of the bankruptcy court’s jurisdiction is 28 U.S.C. §§ 1334 and 157....”13

Section 1334 grants the federal district courts jurisdiction over four types of bankruptcy matters: (1) “cases under title 11,” (2) “proceedings arising under title 11,” (3) proceedings “arising in” a case under title 11, and (4) proceedings “related to” a case under title ll.14 The *304first category refers to the bankruptcy petition itself.15 The second, third, and fourth categories, all listed in § 1334(b), “operate conjunctively to define the scope of jurisdiction. Therefore, it is necessary only to determine whether a matter is at least ‘related to’ the bankruptcy.”16 A proceeding is “related to” a bankruptcy if “the outcome of that proceeding could conceivably have any effect on the estate being administered in bankruptcy.” 17

By way of district-court referral, the bankruptcy court may “hear and determine” certain matters falling within the jurisdictional grant of § 1334.18 Specifically, § 157(b)(1) gives bankruptcy courts full judicial power over “all cases under title 11 and all core proceedings arising under title 11, or arising in a case under title 11, referred under ... this section.19 Non-core proceedings that are “otherwise related to a case under title 11” may be heard by a bankruptcy judge, but any final order or judgment must be entered by the district court.20 Thus, if a matter within the broad scope of § 1334(b) satisfies the more precise notion of a core proceeding, § 157 authorizes the bankruptcy court to decide the matter and enter a final judgment. Although the statute does not define core proceedings, subsection (b)(2) does provide a nonexclusive list of examples.21 Moreover, we have held that § 157 equates core proceedings with the categories of “arising under” and “arising in” proceedings; therefore, a “proceeding is core under section 157 if it invokes a substantive right provided by title 11 or if it is a proceeding that, by its nature, could arise only in the context of a bankruptcy case.”22

With this general framework in mind, we acknowledge that the post-confirmation posture of this case complicates our analysis somewhat. Section 1334 does not expressly limit bankruptcy jurisdiction upon plan confirmation. Consequently, several courts have adapted the broad “related to” test for application in post-confirmation disputes.23 Those courts find that a proceeding falls within the jurisdictional grant if it has “a conceivable effect on the debtor’s ability to consummate the confirmed plan....”24 In the recent case of In re Craig’s Stores of Texas, Inc., however, we rejected this expansive view in favor of a “more exacting theory”: “After a debtor’s reorganization plan has been confirmed, the debtor’s estate, and thus bankruptcy jurisdiction, ceases to exist, other than for matters pertaining to the implementation or execution of the plan.”25 Al*305though we can imagine cases where the two approaches would produce different results, bankruptcy jurisdiction existed over the Appellants’ motion in this case, even under the narrower test.

The U.S. Brass reorganization plan has been substantially consummated, but it has not been fully consummated. The Appellants still have an obligation to resolve the Shell/CNA claims, and that obligation is at the heart of this dispute. Although section 8.20(b) of the plan provides that Shell and CNA are entitled to assert their claims “by institution of litigation in a court of competent jurisdiction,”26 they now intend to submit the claims to binding arbitration. Thus, in opposition to the motion, the Insurers rely on the Bankruptcy Code’s prohibition on modification of a substantially consummated plan of reorganization.27 The Appellants contend, on the other hand, that their proposed agreement — including the arbitration provision — is fully consistent with the plan. Bankruptcy law will ultimately determine this dispute, and the outcome could affect the parties’ post-confirmation rights and responsibilities. Furthermore, this proceeding will certainly impact compliance with or completion of the reorganization plan. Consequently, the Appellants’ motion pertains to the plan’s implementation or execution and therefore satisfies the Craig’s Stores test for post-confirmation jurisdiction.

Having found that subject matter jurisdiction exists over the parties’ dispute, we must now decide whether the bankruptcy court could hear and determine this matter as a core proceeding.28 To this end, we have noted already that a proceeding is core if it arises under title 11 or arises in a case under title 11. In their motion, the Appellants invoke 11 U.S.C. § 1142(b), which authorizes post-confirmation bankruptcy orders “necessary for the consummation of the plan.”29 Some courts hold that when a movant seeks an order pursuant to § 1142(b), the proceeding arises under title ll.30 We find, how*306ever, that § 1142(b) does not confer substantive rights so much as it empowers the bankruptcy court to enforce the unperformed terms of a confirmed plan.31 Thus, proceedings within the contemplation of § 1142(b) are more appropriately viewed as “arising in” a case under title 11.

“ ‘[AJrising in’ proceedings are those that are not based on any right expressly created by title 11, but nevertheless, would have no existence outside of the bankruptcy.”32 Proceedings invoking the bankruptcy court’s statutory authority to enter orders necessary for the consummation of a confirmed plan meet this criteria because the authority can be exercised only in the context of a bankruptcy case. In other words, such proceedings arise only in bankruptcy. Here, the Appellants sought an order pursuant to § 1142(b), and, although the Insurers opposed the requested relief, each side argued that a ruling in its favor was necessary to the implementation or execution of the U.S. Brass plan. This dispute would not exist outside of this bankruptcy case. As a result, the proceeding on the Appellants’ motion constitutes a core proceeding.33

In sum, the present matter falls within the jurisdictional grant of 28 U.S.C. § 1334 and qualifies as a core proceeding over which the bankruptcy court had full judicial power. Furthermore, under 28 U.S.C. § 158, the district court had jurisdiction to review the bankruptcy court’s order denying the motion,34 and we now have jurisdiction over this appeal.35

III. ANALYSIS

A. Standard of Review

“This Court, acting as a second review court, reviews the bankruptcy court’s findings of fact under the clearly erroneous standard, and the bankruptcy court’s conclusions of law de novo.”36 And we review a bankruptcy court’s decision to approve or disapprove a settlement under *307an abuse of discretion standard.37 In the present case, the bankruptcy court determined that the proposed agreement was not a settlement, but rather an attempt to modify a substantially consummated plan of reorganization in contravention of 11 U.S.C. § 1127(b). This determination presents a mixed question of law and fact that is subject to de novo review.38

B. The Appellants ’ Motion

“[Arbitration is simply a matter of contract between the parties; it is a way to resolve those disputes — but only those disputes — that the parties have agreed to submit to arbitration.”39 But the Appellants’ contractual freedom is not unlimited. Because the U.S. Brass reorganization plan functions as a contract in its own right, obligations created by the plan potentially constrain the Appellants’ ability to submit the Shell/CNA claims to arbitration.40 The gravamen of the Appellants’ argument, then, is that the agreement to arbitrate the claims is a “settlement” within the contemplation of plan section 8.20(b). We note, as a preliminary matter, that section 8.20(b) does not require bankruptcy-court approval of a settlement liquidating the Shell/CNA claims.41 So if the agreement is indeed consistent with the plan, the question becomes why did the Appellants file the motion for approval.

The answer lies in the Bankruptcy Code. Section 1127(b) “allows post-confirmation modification of a Chapter 11 plan after notice and a hearing, so long as the proposed modification is presented to the Court ‘before substantial consummation of such plan.’ The section operates to prohibit modification once ‘substantial consummation’ has occurred.”42 This court has already determined that the U.S. Brass plan has been substantially consummated.43 Thus, § 1127(b)’s prohibition applies, and the Appellants concede that they presented their proposed agreement to the bankruptcy court because the Insurers took the position that it would, in fact, modify the plan. We therefore find that the bankruptcy court correctly concluded, from its mere involvement in this post-confirmation dispute, that the true issue is whether the proposed agreement constitutes an impermissible attempt to modify the plan, despite the Appellants’ characterization of the agreement as a settlement.

We also agree with the bankruptcy court’s holding on this issue. As confirmed, the plan contemplates liquidation of the claims through “litigation in a court of competent jurisdiction” rather than ar*308bitration. Although the plan permits the Appellants to end the required litigation by settling the claims, the Insurers were confident at the time of confirmation that a voluntary settlement reducing the claims to a fixed dollar amount would be subject to their approval under the terms of the policies. And if the Appellants chose, instead, to pursue the claims to final judgment, the proceedings would be adversarial and each side would enjoy the safeguards associated with a judicial forum. Accordingly, under either method of determination, “settlement or final judgment,” there were factors minimizing the risk of collusion. The Insurers now fear that, through arbitration, the Appellants will collusively generate a binding award that is inconsistent with the facts and applicable law, but enforceable against the Insurers as if it were a final judgment. Whether this fear is well-founded is immaterial, for we are persuaded that the Insurers would not have withdrawn their objections to confirmation if the plan’s process for resolving the Shell/ CNA claims did not ensure the substantive, procedural, and evidentiary protections of litigation, including U.S. Brass and Eljer’s right to appeal on the basis of legal error. In short, the Insurers wanted litigation, and that is what they received in the confirmed plan.

In reaching this same conclusion, the bankruptcy court found that arbitration of the Shell/CNA claims “was not an option specifically contemplated and negotiated by the parties at confirmation.”44 We attributed similar significance to the parties’ pre-confirmation interactions in our March 1999 dismissal of an appeal from the Confirmation Order, relying, in part, on the “negotiations of the parties interested in the Chapter 11 case and the bargains they secured by voting in favor of the plan.”45 Because the plan provides that the U.S. Brass/Eljer policies are the sole source of recovery for any proven Shell/CNA claims, the dispute resolution process was of critical importance to the Insurers, hence their active participation in plan negotiations. Aware of the Insurers’ exposure and their concern with preventing collusive behavior among the parties responsible for liquidating the claims, the bankruptcy court did not confirm the plan until the Insurers withdrew their objections. To substitute arbitration for litigation at this point would alter the bargain the Insurers secured in exchange for their approval of the plan — in violation of § 1127(b).

In addition to approval of the substitution, the Appellants also sought a bankruptcy-court order tolling the limitations period of plan section 8.21. This component of the motion was undoubtedly a response to the Insurers’ position that arbitration of the Shell/CNA claims over their objections would contravene the “cooperation” and “no action” provisions of the U.S. Brass/Eljer policies. Under the proposed agreement, Shell and CNA would dismiss the New Jersey and Texas lawsuits — actions that had been timely instituted in accordance with the plan.46 If approved, *309the extension of the limitations period would allow the Appellants to refile those actions should arbitration of the claims ultimately give rise to valid coverage defenses.47 Yet they could avoid this risk altogether by complying with the clear terms of the plan, and so their request is self-defeating. By its very nature, the tolling provision would modify section 8.21’s requirement that litigation commence within 180 days of the plan’s effective date. Therefore, the bankruptcy court properly determined that 11 U.S.C. § 1127(b) prohibited it from granting the extension.

Because the Appellants’ proposed agreement would alter the parties’ rights, obligations, and expectations under the plan, the bankruptcy court’s denial of the motion was correct as a matter of law.

IV. CONCLUSION

For the foregoing reasons, we affirm the district court’s judgment affirming the bankruptcy court’s denial of the “Motion for Order in Aid of Consummation of Plan and for Approval of Settlement of Plumbing Claims of Shell Oil Company and Hoechst Celanese Corporation.”

AFFIRMED.