Michelle Gomez Berezowsky and Pablo Angel Rendon Ojeda, Mexican nationals, are locked in a custody dispute over their six-year-old son, “PARB.” Berezowsky filed a Hague Convention petition in the *250Southern District of Texas, arguing that Rendon had wrongfully removed PARB from his habitual residence (purportedly Mexico). The district court ruled in her favor, and Rendon appealed. We vacated and remanded with instructions to dismiss.1 After the district court dismissed the suit without further comment, Rendon moved to amend the judgment and ultimately appealed once more to this court, arguing that the district court should have ordered Berezowsky to return PARB to him. Finding no reversible error in the judgment below, we AFFIRM.

I

Since shortly after PARB’s birth in May 2009, Berezowsky and Rendon have been fighting over the child in state, federal, and foreign courts.2 The events underlying the present appeal began in fall 2012, when, amidst conflicting 'rulings from a Texas state district court and several Mexican courts, Rendon took PARB from his school in Mexico and brought him to Texas. Berezowsky then filed a Hague Convention petition in the Southern District of Texas, alleging that Rendon had illegally removed PARB from his habitual residence.3 The district court agreed and ordered PARB returned to Berezowsky,4 Rendon complied, and Berezowsky, with the district court’s permission, left for Mexico with PARB.

In the meantime, Rendon appealed, asking that PARB be returned to him. In an August 2014 decision (hereinafter Ojeda I), we overturned the district court’s judgment, finding that “Berezowsky failed to meet her burden of establishing that Mexico was PARB’s place of habitual residence.”5 We concluded, in relevant part, that “[f]or the reasons stated in this opinion we VACATE the district court’s order and REMAND with instructions to dismiss.” 6 The accompanying mandate stated that “[i]t is ordered and adjudged that the judgment of the District Court is vacated, and the cause is remanded to the District Court for further proceedings in accordance with the opinion of this Court.”

On remand, the district court succinctly “ORDERED THAT the [District] Court’s Order for the return of the child [to Bere-zowsky] ... is VACATED and this action is DISMISSED.” Rendon timely filed a Rule 59(e) motion to amend the judgment, asking the court to order Berezowsky to return PARB to him in light of the dismissal. The district court denied the motion, and Rendon again appealed.

*251ii

We review the denial of a Rule 59(e) motion for abuse of discretion.7 “Under Rule 59(e), amending a judgment is appropriate (1) where there has been an intervening change in the controlling law; (2) where the movant presents newly discovered evidence that was previously unavailable; or (3) to correct a manifest error of law or fact.”8 “ ‘Manifest error’ is one that ‘is plain and indisputable, and that amounts to a complete disregard of the controlling law’ ” or “an obvious mistake or departure from the truth.”9

The same abuse of discretion standard and three-prong test govern a district court’s decision to deviate (or not) from a mandate.10 “We review de novo whether a district court accurately interpreted and applied the directives of an appellate court’s mandate.”11

III

Rendon and Berezowsky offer starkly different readings of our Ojeda I mandate. Rendon claims that the mandate unambiguously required the district court to order PARB’s return to him. On this reading, the district court “manifestly err[ed]” in refusing to enter such an order, rendering its denial of Rendon’s 59(e) motion an abuse of discretion. Rendon plausibly claims that any other reading would allow his victory on appeal to become a de facto defeat, impermissibly violating the spirit (if not the letter) of our mandate;12 as he points out, “[t]he current reality on the ground is Berezowsky retains possession of [PARB] solely by virtue of a Return Order which has been vacated by this Court.”13

Berezowsky claims that the Ojeda I mandate forbade the district court from *252issuing a re-return order. She offers three substantive rejoinders to Rendon’s arguments.14 First, she argues that both we and the district court were powerless to order a re-return, because the Hague Convention does not contemplate such a remedy. It is true that neither the Convention nor its implementing legislation, the International Child Abduction Remedies Act,15 articulates a re-return right, or, indeed, appellate remedies or procedures of any sort.16 But the federal courts do not need the Convention’s permission to issue a re-return order. As the Supreme Court recognized in Chafin v. Chafin, a re-return order is “typical appellate relief,” as it simply requires “that the Court of Appeals reverse the District Court and that the District Court undo what it has done.”17 The federal courts have inherent equitable power to order such relief.18

Second, Berezowsky argues that the Ojeda I court’s failure to explicitly order a re-return, despite Rendon’s request for one, should be interpreted as an implicit decision not to allow a re-return order, which in turn prevented the district court from ordering that relief. We find this interpretation plausible, but note that only “matters which were ‘decided by necessary implication [or] explicitly’” are off-limits on remand.19 Rendon’s request demonstrates at a minimum that our silence as to a re-return order was deliberate, since the request alerted us to the possibility of such an order. But even if our silence was deliberate, it does not necessarily follow that our silence implied rejection of Rendon’s request and foreclosed the district court from granting it.

Third, and relatedly, Berezowsky argues that the text of our mandate must be construed strictly; because the text does not expressly contemplate a re-return order, she claims, no such order may issue. Berezowsky points to the principle that “[t]he mandate rule requires a district court on remand to effect [the] mandate and to do nothing else,”20 and argues that *253the order to “dismiss” precluded further action by definition. But her definitional argument is questionable,21 and the notion that the district court could “do nothing else” adds little, since our mandate could plausibly be interpreted to implicitly require or permit a re-retum order (as discussed above).

IV

Given the above, we find neither Bere-zowsky’s nor Rendon’s interpretation of our Ojeda I mandate entirely compelling. Moreover, we have found no binding precedent addressing how a mandate “vacating] ... and remanding] with instructions to dismiss” should be parsed.22 Given this, we conclude that Ojeda I neither required nor forbade a re-return order. Rather, we simply did not decide in that case whether or not a re-return order was warranted. Because a lower court “is free to decide matters which are left open by the mandate,” the decision to issue or deny a re-return order was therefore the district court’s.23

The district court decided not to issue a re-return order. As noted above, its subsequent refusal to amend the judgment (which provides the basis of the present appeal) is reviewed for abuse of discretion, and amendment is appropriate if the controlling law has changed, if new evidence is available, or if the initial decision was manifestly erroneous as a matter of law or fact. But Rendon does not allege new evidence or a change in controlling law, and the district court’s decision was not legally or factually erroneous. The law of the case did not compel a re-return order, and the court reasonably could have concluded on these facts that the equities did not favor a re-return order. As three Justices noted in a concurrence in Chafin, re-return orders may prolong and fracture custody proceedings, and “‘shuttling children back and forth between parents and across international borders may be detrimental to those children’ whose welfare led [to] the *254[Hague] Convention.”24 Citing these concerns, the Ninth Circuit recently refused to issue a re-return order after overturning a district court’s Hague Convention decision, in what appears to be the only federal appellate case addressing the propriety of such an order.25

The district court did not abuse its discretion in refusing to issue a re-return order. We therefore decline to disrupt the status quo.26 The judgment of the district court is AFFIRMED.

concurring in the judgment:

This Hague Convention1 proceeding is but the latest chapter in a multi-volume cross-border custody dispute spanning the courts of Texas, the United States, and Mexico. See Berezowsky v. Ojeda (Ojeda I), 765 F.3d 456, 459-65 (5th Cir. 2014) (recounting the involvement of “at least 12 different courts”). Deploying the Hague Convention’s “return” remedy, the district court ordered respondent Pablo Angel Rendon Ojeda to return his then-three-year-old son PARB to PARB’s mother, petitioner Michelle Gomez Berezowsky, in Mexico. The district court denied the father’s stay motion and PARB was returned immediately, even as the father appealed the return order to our court. We ultimately vacated the return order, holding that a prerequisite to the Hague Convention return remedy was absent because Mexico was not PARB’s place of habitual residence. Id. at 459; see Convention art. 3(a). But vacating the order did not undo its practical effect, which by then was already complete: PARB remained — and, as far as we know, remains now — in Mexico with his mother as a result of the order that we held was erroneous.

Out of concern that children “would lose precious months when [they] could have been readjusting to life in [their] country of habitual residence,” the Supreme Court has discouraged courts from routinely staying return orders pending their final resolution on appeal. Chafin v. Chafin, — U.S. -, 133 S.Ct. 1017, 1027, 185 L.Ed.2d 1 (2013); accord id. at 1029-30 (Ginsburg, J., concurring). Denying a stay, however, entrenches the return order while it may yet be vacated. See, e.g., Redmond v. Redmond, 724 F.3d 729 (7th Cir. 2013) (reversing already-executed return order where stay had been denied); Larbie v. Larbie, 690 F.3d 295 (5th Cir. 2012) (reversing already-executed return order where no stay had been sought). “Where no stay is ordered, the risk of a two-front battle over custody will remain real.” Chafin, 133 S.Ct. at 1030 & n.4 (Ginsburg, J., concurring) (citing the rival custody proceedings in Larbie). Cases like this one illustrate the truth of this statement.

*255With PARB already returned to Mexico, Rendon’s appeal continued to present a live controversy because of the possibility that we might “reverse the District Court and that the District Court [might] undo what it ha[d] done” — that is, order that PARB be “re-returned” to the United States. Chafin, 133 S.Ct. at 1024; see Ojeda I, 765 F.3d at 464 n.4. Under Chafin, once we did reverse the district court, it would have been appropriate for the district court to consider PARB’s re-return. Nevertheless, as the majority opinion explains, because our mandate did not discuss the issue and because the district court may have considered and rejected re-return, the district court did not abuse its discretion in denying Rendon’s Rule 59(e) motion for re-return. I consequently concur in the judgment.

This case provides yet another example of the problems that can occur when federal courts address Hague Convention return petitions. The Hague Convention’s role within the broader context of cross-border custody disputes is to undo an abduction so as to “facilitate custody adjudications, promptly and exclusively, in the place where the child habitually resides.” Chafin, 133 S.Ct. at 1028 (Ginsburg, J., concurring) (citing Convention arts. 1, 3). But time and again federal courts have struggled in that task, likely because of both the substantive law involved and the procedural strictures of federal court litigation. Cf. Redmond, 724 F.3d at 749 (Easterbrook, J., dubitante) (“It is time for this federal overlay to end and the subject be returned to the domestic-relations' apparatus of Illinois and Ireland, where it should have been all along.”).

For example, we have struggled to heed our own admonition that, in light of the Hague Convention’s limited purview, courts “must not cross the line into a consideration of the underlying custody dispute.” Sealed Appellant v. Sealed Appellee, 394 F.3d 338, 344 (5th Cir. 2004); see 22 U.S.C. § 9001(b)(4) (“The Convention and this chapter empower courts in the United States -to determine only rights under the Convention and not the merits of any underlying child custody claims.”). In spite of that straightforward directive, we recently gave one of the Hague Convention exceptions an interpretation that we acknowledged could “embroil the state of refuge in the underlying custody dispute.” Rodriguez v. Yanez, 817 F.3d 466, 475 & n.33 (5th Cir. 2016) (interpreting the exception for when “the child objects to being returned”); see Convention art. 13. We likewise recently joined the Second and Ninth Circuits in adopting a multi-factor test for the Convention’s “well-settled” defense that requires courts to weigh custody-type considerations, including “the stability and duration of the child’s residence in the new environment,” “whether the child attends school or day care consistently,” “the child’s participation in com.munity or extracurricular activities,” and the respondent parent’s “employment and financial stability.” Hernandez v. Garcia Pena, 820 F.3d 782, 787-88 (5th Cir. 2016); see John DeWitt Gregory, Peter Nash Swisher & Robin Fretwell Wilson, Understanding Family Law 522-23 (4th ed. 2013) (listing factors state courts typically consider when adjudicating child custody). These are complicated and wrenching areas of substantive law with which we have little expertise.

Nor-are we well-suited to the prompt resolution that the Hague Convention envisions we will achieve. The Convention sets six weeks as the target time for judicial disposition of a petition, see Convention art. 11, but in 2008, from the filing of a Hague Convention petition in the United States, “the average time taken to reach a first instance decision was 209 days compared with 441 days to finalise a case that was appealed.” Nigel Lowe, A Statistical Analysis of Applications Made in 2008 *256Under the Hague Convention of 25 October 1980 on the Civil Aspects of International Child Abduction — Part III, National Reports 207 (2011). In one prominent and particularly unfortunate example, after the Supreme Court held that the petitioning parent could seek a return order in Abbott v. Abbott, 560 U.S. 1, 130 S.Ct. 1983, 176 L.Ed.2d 789 (2010), the district court had to dismiss the petition on remand because, during the nearly-six-year course of the litigation, the child had turned sixteen — at which point the Convention ceased to apply. Gregory, Swisher & Wilson, supra, at 515 n.117.

Justice Ginsburg has suggested a legislative fix by which district court return orders could be appealed only with leave from the court of appeals, with the return order routinely stayed if leave is granted. Chafin, 133 S.Ct. at 1030 (Ginsburg, J., concurring). In the meantime, any parent with a foreign custody judgment can keep federal courts out of the equation altogether by seeking the enforcement of that judgment in the courts of any of the fifty states, all of which have adopted either the Uniform Child Custody Jurisdiction and Enforcement Act (UCCJEA) or its predecessor statute. Gregory, Swisher & Wilson, supra, at 501. See generally Robert G. Spector, International Abduction of Children: Why the UCCJEA Is Usually a Better Remedy than the Abduction Convention, 49 Fam. L.Q. 385 (2015) (contrasting the Hague Convention and UCCJEA regimes). As for the parties here, I am reminding of my colleague’s admonition in our previous encounter with this case: “ You owe your child better than this’ and [we] urge both parents to make a concerted effort to settle this matter in PARB’s, not their own, best interests.” Ojeda I, 765 F.3d at 476 (Haynes, J., dissenting).