
578 F.3d 39 (2009)
Antwan CRAWFORD; Darrick Wilson; Anthony Tucker, Plaintiffs,
Mac S. Hudson; Derrick Tyler, Plaintiffs, Appellees,
v.
Harold W. CLARKE, Commissioner of the Massachusetts Department of Correction, Defendant, Appellant,
Kathleen Dennehy, Defendant.
No. 08-2100.
United States Court of Appeals, First Circuit.
Heard May 6, 2009.
Decided August 24, 2009.
*41 Richard C. McFarland, Legal Division, Department of Correction, with whom Nancy Ankers White, Special Assistant Attorney General, was on brief for appellant Harold W. Clarke.
Michael Kendall, with whom Neal E. Minahan, David Quinn Gacioch, and McDermott Will & Emery LLP, were on brief for appellees Hudson and Tyler.
Before TORRUELLA, and SELYA, Circuit Judges, and TASHIMA,[*] Senior Circuit Judge.
TORRUELLA, Circuit Judge.
The Commissioner of the Massachusetts Department of Correction (the "DOC") appeals an injunction entered in favor of the plaintiffs-appellees Mac S. Hudson and Derrick Tyler (together, the "Plaintiffs"). After careful consideration, we affirm.
The Plaintiffs are Muslim inmates in the custody of the DOC. In 2001, they filed a non-class action complaint, later amended, asserting that the Commissioner violated their right to freely exercise their religion.
At issue in this appeal is the ability to participate in Jum'ah, which is "a Friday group prayer that is obligatory for Muslims." Hudson v. Dennehy, 538 F.Supp.2d 400, 404 n. 4 (D.Mass.2008). At the time of the filing of their Amended Complaint, the Plaintiffs were housed in an special management unit ("SMU") at MCI-Cedar Junction known as "Ten Block." SMUs are housing units separate from the general population of the prison "in which inmates may be confined for reasons of administrative segregation, protective custody, or disciplinary detention." 103 Mass.Code Regs. 423.06. Plaintiffs alleged that, "[w]hile segregated, [they] are denied the right to attend mandatory Jumah services." They further alleged that "[p]risoners with televisions may participate in the prison's Jumah services, which are broadcast via closed-circuit televisions," but that "[t]he DOC presently denies [the Plaintiffs] access to a television and, therefore, access to Jumah services." In their prayer for relief, the Plaintiffs sought "a permanent injunction ordering Defendant ... to allow Plaintiff to attend all Jumah services either in person or via closed-circuit television."
The district court conducted a six-day bench trial concerning Plaintiffs' claims.[1] After trial, the district court applied the Religious Land Use and Institutionalized Persons Act ("RLUIPA"), which provides that:
No government shall impose a substantial burden on the religious exercise of a person residing in or confined to an institution, as defined in [42 U.S.C. § 1997], even if the burden results from a rule of general applicability, unless the government demonstrates that imposition of the burden on that person

*42 (1) is in furtherance of a compelling governmental interest; and
(2) is the least restrictive means of furthering that compelling governmental interest.
42 U.S.C. § 2000cc-1(a). The district court ruled that "[t]he DOC's ban on personal participation in Jum'ah services by inmates confined in Ten Block serves the compelling State interest of rehabilitating prisoners and promoting good order." Hudson, 538 F.Supp.2d at 412. However, the court further ruled that "[t]he ban on participation by Ten Block inmates in Jum'ah services by closed-circuit television is not the least restrictive means of vindicating" the compelling state interests of the DOC, noting that "the DOC does not contend that there is any technical reason that prevents the broadcast of Jum'ah services by closed-circuit television to Muslim inmates in Ten Block." Id. at 412 & n. 24.
The district court later entered an injunction requiring closed-circuit broadcasting of Jum'ah "[w]henever Plaintiffs are housed in the Special Management Unit,"[2] not limiting its injunction to the SMU at MCI-Cedar Junction. When the Commissioner sought clarification, the district court confirmed that the injunction required closed circuit television broadcasts of Jum'ah services in any SMU in which Plaintiffs may be housed in the future.
The Commissioner then moved for reconsideration, attaching the affidavit of Jeffrey Quick, the DOC's Director of Resource Management (the "Quick Affidavit"). The Quick Affidavit outlined the significant technical, operational, physical plant, and cost impediments to providing closed-circuit television broadcasts to certain SMUs located at prisons other than MCI-Cedar Junction. The Quick Affidavit further noted that Tyler was "presently incarcerated in the general population of MCI-Cedar Junction," and that Hudson was "presently incarcerated at [Old Colony Correctional Center] and is housed in the general population."
That same day, the district court denied the motion for reconsideration, stating:
After hearing, the motion is denied without prejudice. Plaintiff Hudson is currently confined in general population at the Old Colony Correctional Facility. Accordingly, there is no actual controversy appropriate for judicial resolution.
The Commissioner subsequently filed a notice of appeal that listed only the denial of the motion for reconsideration.
As an initial matter, the Plaintiffs contend that the only decision on appeal is the district court's denial of the Commissioner's motion for reconsideration. They point out that Federal Rule of Appellate Procedure 3 provides that "[t]he notice of appeal must ... designate the judgment, order, or part thereof being appealed," Fed. R.App. P. 3(c)(1)(B), and the notice of appeal here only lists the denial of the motion for reconsideration.[3] Indeed, "an *43 appeal from an order denying such a motion is generally not considered to be an appeal from the underlying judgment." Chamorro v. Puerto Rican Cars, Inc., 304 F.3d 1, 3 (1st Cir.2002) (discussing a motion for reconsideration).
However, "our precedents encourage us to construe notices of appeal liberally and examine them in the context of the record as a whole." Id. Although the notice of appeal only lists the denial of the motion for reconsideration, it references the "Final Judgment with Regard to Broadcast of Jum'ah Services in Special Management Units Other Than Ten Block." "Read in context, this reference is consistent with a desire to have this court review the propriety of the" injunction with respect to Jum'ah services. Id. at 4 (noting that notice of appeal only listing denial of motion for reconsideration also referenced dismissal for want of prosecution, which reflected an intent to reach the dismissal). Moreover, "both sides have fully briefed the merits, and undertaking appellate review of the original order ... would not unfairly prejudice" the Plaintiffs. See id. Although we recognize that "rescue missions are not automatic, and litigants will do well to draft notices of appeal with care," we will give the Commissioner the benefit of the doubt and treat the injunction itself as properly before us. Id. at 3.
"[T]he scope of [an] injunction is reviewed for abuse of discretion." Esso Standard Oil Co. v. López-Freytes, 522 F.3d 136, 142-43 (1st Cir.2008). The Commissioner contends that the district court erred by entering a prospective injunction that applies to all SMUs without making findings as to whether SMUs other than Ten Block are suitable for closed circuit television broadcasts of Ju'mah services. Thus, according to the Commissioner, the prospective injunction violates the Prison Litigation Reform Act (the "PLRA"), which requires "prospective relief" to be "narrowly drawn, extend[] no further than necessary to correct the violation of the Federal right, and [be] the least intrusive means necessary to correct the violation of the Federal right." 18 U.S.C. § 3626(a)(1)(A). The Commissioner also relies on RLUIPA, contending that the DOC can demonstrate that it has a "compelling governmental interest" in not providing closed circuit broadcasting of Ju'mah services to SMUs other than Ten Block given the high cost of providing such services, see Baranowski v. Hart, 486 F.3d 112, 125 (5th Cir.2007) (compelling interest standard met under RLUIPA when prison budget not adequate to cover Kosher meals), and the resultant imposition such a requirement would put on the Commissioner's discretion to assign the Plaintiffs to different facilities.
We conclude that the district court did not abuse its discretion. Although the Plaintiffs' allegations in their Amended Complaint focused on the lack of closed-circuit broadcasting in Ten Block, their prayer for relief was not limited to Ten Block. Plaintiffs plainly sought system-wide relief. Despite being on notice of this claim for relief, the Commissioner did not present during the bench trial any of the evidence contained in the Quick Affidavit, despite having the "onus" to show that the burden it placed on the Plaintiffs' religious exercise "furthers a compelling governmental interest and ... that the burden is the least restrictive means of achieving that compelling interest." Spratt v. R.I. Dep't of Corrs., 482 F.3d 33, 38 (1st Cir. 2007) (holding that, under RLUIPA, once a plaintiff establishes a substantial burden on the exercise of his or her religion, the "onus shifts to the government"). Instead, the Commissioner provided evidence that the DOC's system-wide policy banning televisions in SMUs was due to (1) the *44 temporary nature of SMU detention; (2) the security risks associated with having a television in an inmate's cell; and (3) the DOC's desire to avoid any incentive for inmates to seek SMU detention. A witness, MCI-Cedar Junction Deputy Superintendent Lisa Mitchell, testified that there was no technical reason that prevents the broadcast of Jum'ah services by closed-circuit television to Muslim inmates in Ten Block, but the Commissioner did not provide evidence that this was not the case for other facilities. In fact, the Commissioner provided testimony, through its Acting Deputy Commissioner, John Marshall, that the DOC sought to create a universal SMU policy to alleviate any differences in SMU policies among various facilities.
Given the record before it, the district court tailored an injunction that was consistent with the PLRA's directive that all "prospective relief" be "narrowly drawn," "extend[ ] no further than necessary to correct the violation of the Federal right," and be the "least intrusive means necessary to remedy the violation of a Federal right." 18 U.S.C. § 3626(a)(1)(A). The Plaintiffs established a substantial burden on the exercise of their religion, and, in evaluating whether to enable Plaintiffs to participate in Jum'ah services in person or provide closed-circuit broadcasting of such services, the district court found that providing closed-circuit broadcasting was the least intrusive means to alleviate that burden on the Plaintiffs. See Hudson, 538 F.Supp.2d at 412. The Commissioner put nothing in the record to differentiate facilities other than Ten Block on the issues of compelling governmental interest or least restrictive means. Moreover, under RLUIPA, the Commissioner had the burden to put forward his additional evidence at trial and failed to do so. See Spratt, 482 F.3d at 38. The district court is not a mind reader, and, given the Commissioner's failure to provide the additional evidence contained in the Quick Affidavit at trial, we conclude that no abuse of discretion occurred in framing the injunction.
For substantially the same reasons, the district court did not abuse its discretion in denying the Commissioner's motion for reconsideration. "We review a trial court's decision denying a Rule 59(e) motion to alter or amend a judgment for manifest abuse of discretion." Vasapolli v. Rostoff, 39 F.3d 27, 36 (1st Cir.1994). We have emphasized that Rule 59(e) "does not provide a vehicle for a party to undo its own procedural failures, and it certainly does not allow a party to introduce new evidence or advance arguments that could and should have been presented to the district court prior to the judgment." Aybar v. Crispin-Reyes, 118 F.3d 10, 16 (1st Cir.1997). As the Commissioner sought to introduce evidence that he could have advanced at trial but chose not to, the district court's denial of the motion for reconsideration did not amount to an abuse of discretion.
We conclude by emphasizing that, under Federal Rule of Civil Procedure 60(b)(5), the Commissioner is free to move for relief from the injunction when "applying it prospectively is no longer equitable." Fed. R.Civ.P. 60(b)(5); see also Esso, 522 F.3d at 149-50 (rejecting claim that "the scope of [the] injunction was overly broad because it lacks an express provision for termination of the injunction," noting the availability of Rule 60(b)(5)). Moreover, under the final judgment entered in this case, the district court retained jurisdiction "for the purpose of enabling any party to this Judgment to apply to the Court for... the modification of the injunctive provisions of this Judgment." In fact, the district court, in its denial of the Commissioner's *45 motion for reconsideration, demonstrated a willingness to address the injunction should circumstances require it, that is, if the Plaintiffs (or either of them) are about to be housed in an SMU other than Ten Block. Thus, if and when the time comes, the Commissioner will have an avenue to press its concerns.
For the foregoing reasons, the entry of the injunction in this case is affirmed.
AFFIRMED.
NOTES
[*]  Of the Ninth Circuit, sitting by designation.
[1]  The trial encompassed other religious freedom claims as well, but the district court's resolution of those claims is not challenged on appeal.
[2]  The injunction states in relevant part:

Whenever Plaintiffs are housed in the Special Management Unit, Defendant shall provide access to a closed circuit television set that displays, through sound and images, a live broadcast of such communal Jum'ah services as are regularly held on each and every Friday for the duration of their incarceration....
[3]  The notice states in full:

Notice is hereby given that Harold W. Clarke, Commissioner of the Massachusetts Department of Correction, defendant in the above named case, hereby appeals to the United States Court of Appeals for the First Circuit from the Order denying Defendant's Motion for Reconsideration of Final Judgment with Regard to Broadcast of Jum'ah Services in Special Management Units Other Than Ten Block, entered in this action on June 19, 2008.
