MESKILL, Circuit Judge:
The principal issue in this pro se appeal is whether state prison officials satisfied due process requirements when they held an inmate in administrative confinement for two days. The pro se plaintiff, Jory Lowrance a/k/a Ya’Qub Shamsid-Deen, appeals from a judgment of the United States District Court for the Northern District of New York, DiBianco, M.J., granting summary judgment in favor of the defendants and dismissing Shamsid-Deen’s complaint alleging that the defendants violated 42 U.S.C. § 1983.1 All of the- defendants, Correction Officer Achtyl, Sergeant Skrocki, Sergeant Lay, Lieutenant Inserra, Lieutenant Mutz, Correction Officer Sroka, and Acting Deputy Superintendent for Security Cunningham, worked at Sha-wangunk Correctional Facility (Shawangunk) at the. time of the incidents giving rise to Shamsid-Deen’s claims. We find Shamsid-Deen’s contentions to be unpersuasive and we affirm the judgment of the magistrate-judge.
BACKGROUND
During an evening meal on August 11, 1991, Shamsid-Deen, an inmate on a low cholesterol diet at Shawangunk, brought hot sauce into the mess hall, exchanged food with another inmate, and used the hot sauce on his food. This conduct violated a rule that had been issued in February 1989 by the Deputy Superintendent for Administrative Services at Shawangunk (Rule). The Rule was supposed to have. been posted in all housing units and mess halls.
Correction Officer Achtyl observed Sham-sid-Deen’s behavior in the mess hall and, as Shamsid-Deen left the mess hall, ordered the inmate to give him the hot sauce. Shamsid-Deen refused and stated that the sauce belonged to him. Achtyl subsequently issued a misbehavior report, charging Shamsid-Deen with three rule violations: disobeying a direct order, bringing food items into the mess hall, and failing to comply with seating and serving policies. As a result of these alleged violations, Shamsid-Deen was placed in administrative confinement, or “keeplock,” some time in the evening of August 11 pending his disciplinary hearing.
During the period of keeplock, Shamsid-Deen sought to speak to several correction officials regarding the propriety of his administrative confinement.. By his own admis[532]*532sion, Shamsid-Deen complained orally to Sergeant Lay and Correction Officer Sroka about his confinement. Shamsid-Deen also concedes that he was advised that he could complain in writing to Cunningham, the Acting Deputy Superintendent for Security, and that he did so. Shamsid-Deen asserts, however, that he never received a reply from Cunningham. Lieutenant Inserra was the Review Officer responsible for reviewing the propriety of Shamsid-Deen’s keeplock status.
At about noon on August 12, 1991, Sham-sid-Deen was served with Achtyl’s misbehavior report. In the afternoon of August 13, 1991, a Shawangunk official held a disciplinary hearing on Achtyl’s charges against Shamsid-Deen. Shamsid-Deen was present and participated in the hearing. The presiding official ultimately dismissed the charges on the ground that the Rule that Shamsid-Deen had allegedly violated had not been distributed and that, therefore, Shamsid-Deen had not known that his actions were prohibited.
Shamsid-Deen filed this section 1983 action against the defendants and asserted that (1) Achtyl had filed the misbehavior report in retaliation for Shamsid-Deen’s previous filing of grievances regarding the special diet program, and (2) the defendants had violated Shamsid-Deen’s due process rights by placing him in administrative segregation awaiting the disciplinary hearing. The defendants subsequently moved for summary judgment on three grounds: (1) Shamsid-Deen’s retaliation claim is conclusory and wholly unsupported, (2) Shamsid-Deen’s prehearing administrative confinement comported with due process requirements, and (3) the defendants are entitled to qualified immunity.
The magistrate judge granted the defendants’ summary judgment motion on the grounds that (1) there was no evidence supporting the claim that the misbehavior report had been filed in retaliation for Shamsid-Deen’s grievances, and (2) the prehearing keeplock had been validly imposed and had satisfied due process requirements. Accordingly, on March 10, 1993, the magistrate judge dismissed Shamsid-Deen’s complaint and entered judgment in favor of the defendants.
Shamsid-Deen filed a motion for reconsideration of the retaliation claim. With his motion, Shamsid-Deen submitted the affidavit of Reginald Troy, an inmate at Shawan-gunk who had been in the mess hall with Shamsid-Deen on August 11. The affidavit stated that, before issuing the misbehavior report against Shamsid-Deen on August 11, Achtyl had told Shamsid-Deen that Achtyl could write better misbehavior tickets than Shamsid-Deen could write grievances. The magistrate judge accepted Shamsid-Deen’s explanation for his delay in producing the Troy affidavit, but refused to disturb its previous judgment on the ground that, even with the new affidavit, Shamsid-Deen had shown no more than that Achtyl may have had a mixed motive for filing the misbehavior report and that, when one of several motives is proper, the state.action must be sustained. See Sher v. Coughlin, 739 F.2d 77, 82 (2d Cir.1984) (“state action taken on the basis of both valid and invalid motivations is not constitutionally tainted by the invalid motive if the action would in any event have been taken on the constitutionally valid basis”).2
Shamsid-Deen challenges the grant of summary judgment against him and from the denial of relief after reconsideration. He contends that the magistrate judge improperly determined that the defendants were entitled to judgment as a matter of law on the retaliation claim and that the defendants had not violated his due process rights during his administrative confinement. The defendants contend, on the other hand, that Shamsid-Deen did not properly perfect his appeal from the magistrate judge’s March 10 judgment and, therefore, that only Shamsid-Deen’s appeal from the magistrate judge’s [533]*533denial of relief after reconsideration of the retaliation issue is properly before us.
DISCUSSION
I. Scope of the Appeal
We first address the defendants’ contention that Shamsid-Deen’s appeal from the March 10 judgment is not properly before us. Following the entry of judgment against him, Shamsid-Deen filed a timely notice of appeal on March 25,1993. The appeal proceeded in this Court and was ultimately dismissed on June 7, 1993, on the ground that Shamsid-Deen had defaulted. On March 22, 1993, however, Shamsid-Deen had filed .a timely motion for reconsideration of the March 10 judgment pursuant to Local Rule 10(m) of the Northern District of New York. On May 27, 1993, after reconsideration, the magistrate judge denied relief and Shamsid-Deen filed a timely notice of appeal on June 14, 1993.
Our determination of whether Shamsid-Deen’s appeal from the March 10 judgment is properly before us turns on the validity of the March 25 notice of appeal. Federal Rule of Appellate Procedure 4(a)(4) provides, in pertinent part:
If a timely motion under the Federal Rules of Civil Procedure is filed in the district court by any party: ... (iii) under Rule 59 to alter or amend the judgment; ... the time for appeal for all parties shall run from the entry of the order denying ... any other such motion. A notice of appeal filed before the disposition of any of the above motions shall have no effect. A new notice of appeal must be filed within the prescribed time measured from the entry of the order disposing of the motion as provided above.3
By operation of this rule, the March 25 notice of appeal became a nullity on the filing of the motion for reconsideration if that motion was a motion to alter or amend the judgment pursuant to Federal Rule of Civil Procedure 59(e).
Although Shamsid-Deen’s motion for reconsideration was not labeled a motion “under Rule 59 to alter or amend the judgment,” several factors persuade us to treat the motion as a Rule 59(e) motion for purposes of Rule 4(a)(4). First, Shamsid-Deen’s motion for reconsideration was filed within ten days after the entry of the judgment of. dismissal, in accordance with Local Rule 10(m) of the Northern District of New York, which provides in pertinent part that “[m]otions for reconsideration ... shall be filed and served not later than ten (10) days after the entry of judgment.” We have recognized that “most substantive motions brought within ten days of the entry of judgment are functionally motions under Rule 59(e).” McCowan v. Sears, Roebuck & Co., 908 F.2d 1099, 1103 (2d Cir.), cert. denied, 498 U.S. 897, 111 S.Ct. 250, 112 L.Ed.2d 209 (1990); see also Osterneck v. Ernst & Whinney, 489 U.S. 169, 174, 109 S.Ct. 987, 990, 103 L.Ed.2d 146 (1989); United States v. Clark, 984 F.2d 31, 34 (2d Cir.1993); Northwestern Nat’l Ins. Co. v. Alberts, 937 F.2d 77, 81 (2d Cir.1991). Second, the relief that Shamsid-Deeri sought was akin to the relief afforded under Rule 59(e). See Clark, 984 F.2d at 34; Northwestern Nat’l Ins. Co., 937 F.2d at 81. Finally, that Shamsid-Deen also might have sought relief under Rule 60(b), on the ground that he had obtained new evidence to support his retaliation claim, does not weaken our conclusion. See McCowan, 908 F.2d at 1103. The motion could at once be both a motion to alter or amend under Rule 59(e) and- a motion for relief from judgment under Rule 60(b).
We thus conclude that Shamsid-Deen’s March 22 motion for reconsideration was a tolling motion for purposes of Rule 4(a)(4). By operation of Rule 4(a)(4), the March 25 notice of appeal was a nullity. This Court’s dismissal of Shamsid-Deen’s initial appeal was done without awareness of the new proceedings in the district court that nullified the first notice. Because by operation of law, [534]*534the initial notice had become a nullity, the dismissal of the original appeal has no pre-clusive effect on the subsequent appeal from the denial of the Rule 59(e) motion.
The only notice of appeal'that validly confers jurisdiction on this Court, therefore, is Shamsid-Deen’s June 14 notice, which by its terms relates to “the Judgment and Order ... dated ... May 27,1993, ... denying my motion for reconsideration.” Because that “denial” was essentially an affirmance on the merits of the March 10 judgment, or perhaps a modification thereof, see footnote 2, the June 14 notice of appeal must be said to relate to the entire judgment, not simply to the narrow ground on which the magistrate judge denied relief after reconsideration. Indeed, this case differs slightly from those in which courts have interpreted a notice of appeal as relating to the underlying judgment even though that notice of appeal referred merely to a denial of reconsideration involving no review of the merits (rather than referring, as here, to a denial after reconsideration of the merits of the judgment). Cf. Foman v. Davis, 371 U.S. 178, 181, 83 S.Ct. 227, 229, 9 L.Ed.2d 222 (1962) (where notice of appeal from judgment of dismissal was ineffective but subsequent notice of appeal sought review of denial of posh-trial motion to vacate, “[i]t is too late in the day and entirely contrary to the spirit of the Federal Rules of Civil Procedure for decisions on the merits to be avoided on the basis of [the] mere technicalit[y]” that the second notice of appeal did not refer to the judgment itself); United States v. Schwimmer, 968 F.2d 1570, 1574-75 (2d Cir.1992). By contrast, here, Shamsid-Deen’s June 14 notice sought to appeal from the action that the magistrate judge had taken with respect to his motion for reconsideration; because the magistrate judge’s action was effectively to reaffirm or to modify its March 10 judgment of dismissal after reconsideration of the merits, the June 14 notice referring to the denial of reconsideration referred to the entire judgment. Accordingly, the magistrate judge’s judgment in its entirety is properly before us on appeal.
II. The Merits
We review de novo a grant of summary judgment. Olin Corp. v. Consol. Aluminum Corp., 5 F.3d 10, 14 (2d Cir.1993); Gnazzo v. G.D. Searle & Co., 973 F.2d 136, 138 (2d Cir.1992). It follows, therefore, that we also review de novo the magistrate judge’s reconsideration, on a motion for reconsideration, of the merits of the summary judgment motion.
A. Retaliation Claim
Shamsid-Deen contends that the magistrate judge improperly dismissed his retaliation claim and denied relief on his motion for reconsideration. Shamsid-Deen’s primary claim seems to be that the magistrate judge granted summary judgment before he had completed discovery and that, if given more time, he could have obtained additional evidence in support of his retaliation claim. Indeed, although Shamsid-Deen filed the Troy affidavit with his motion for reconsideration, he asserted in his motion papers that he expected to be able to produce still other affidavits in support of his claim. We are not persuaded.
We review a magistrate judge’s management of discovery with great deference. Lyeth v. Chrysler Corp., 929 F.2d 891, 898 (2d Cir.1991); Hollander v. American Cyanamid Co., 895 F.2d 80, 84 (2d Cir.1990). Here, Shamsid-Deen sought and, on November 10, 1992, was granted a 120 day extension of time for the completion of discovery. In addition, the magistrate judge allowed Shamsid-Deen to file the Troy affidavit with his motion for reconsideration after the judgment had entered. On this record, we conclude that the magistrate judge’s management of discovery was fair and reasonable. We reject, therefore, Shamsid-Deen’s claim that the magistrate judge did not afford him enough time to complete discovery.
Moreover, after reviewing the record as supplemented with the Troy affidavit, we agree that dismissal of the retaliation claim was warranted, and the magistrate judge therefore properly denied relief after reconsideration. The magistrate judge noted that Shamsid-Deen had admitted to engaging in [535]*535the conduct that formed the basis of the misbehavior report. The magistrate judge concluded, therefore, that Shamsid-Deen had established, at best, that Achtyl’s misbehavior report had been motivated by both proper and improper reasons. The magistrate judge then determined, however, citing Sher, 739 F.2d at 82, that because the report would have been issued on proper grounds alone, there had been no constitutional violation.
We agree with this reasoning. In Mt. Healthy City Sch. Dist. Bd. of Educ. v. Doyle, 429 U.S. 274, 287, 97 S.Ct. 568, 576, 50 L.Ed.2d 471 (1977), the Supreme Court held that, in cases in which state action is motivated by both proper and improper reasons, the action may be sustained if it would have been taken even in the absence of the improper reason. See also Berl v. County of Westchester, 849 F.2d 712, 714-15 (2d Cir.1988) (applying dual motivation test to employment discrimination action under Title VII); Sher, 739 F.2d at 82. Under the Mt. Healthy analysis, “the plaintiff carries the initial burden of proving that a discriminatory motive played a substantial part in [the state action at issue]” and then “the burden shifts to defendant to show that it would [have taken the action] even in the absence of the [improper motive].” Berl, 849 F.2d at 714-15.
In this ease, we will assume, without deciding, that Shamsid-Deen met his burden of establishing that a retaliatory motive played a “substantial part” in Aehtyl’s decision to issue a misbehavior report against him. That burden having been met, the burden then shifted to the defendants to establish that Aehtyl would have issued the report in the absence of the improper reason. The magistrate judge implicitly concluded, and we agree, that the defendants had met their burden because it was undisputed that Sham-sid-Deen had in fact committed the prohibited conduct. We have previously noted that the conclusion that the state action would have been taken in the absence of improper motives is “readily drawn in the context of prison administration where we have been cautioned to recognize that ‘prison officials have broad administrative and discretionary authority over the institutions they manage.’ ” Sher, 739 F.2d at 82 (quoting Hewitt v. Helms, 459 U.S. 460, 467, 103 S.Ct. 864, 869, 74 L.Ed.2d 675 (1983)). Accordingly, the magistrate judge properly denied relief on Shamsid-Deen’s motion after reconsideration.
B. Due Process Claim
Shamsid-Deen also challenges the magistrate judge’s grant of summary judgment on and subsequent dismissal of his due process claim. He contends that he did not have an adequate opportunity to be heard during his administrative confinement and that the confinement was arbitrarily imposed, thereby violating his right to substantive due process.4 We disagree.
1. Opportunity To Be Heard
In Gittens v. LeFevre, 891 F.2d 38, 40 (2d Cir.1989), we held that administrative confinement of a prison inmate is not restricted by the Fourteenth Amendment’s Due Process Clause unless the state has created a liberty interest in remaining free from such confinement. We farther determined, that New York had created such a liberty interest by virtue of section 251-1.6(a) of title 7 of the New York Compilation of Codes, Rules & Regulations. Id. (citing N.Y.Comp.Code R. & Regs. tit. 7, § 251-1.6(a) (1988)). That provision permits administrative segregation of inmates only if the correction officer “has reasonable grounds to believe that. an inmate ... represents an immediate threat to the safety, security or order of the facility.” A New York court has held that “reasonable grounds to, believe that an inmate ... represents an immediate threat to the safety, sécurity or order of the facility.” A New York court has held that “reasonable grounds to believe that an inmate ... represents an immediate threat to the safety, security or order” exist when “an officer reasonably believes that a facility rule [536]*536has been violated.” Bowe v. Smith, 119 Misc.2d 458, 455, 465 N.Y.S.2d 391, 393 (Sup.Ct.1983); see also Gittens, 891 F.2d at 40.
We also held in Gittens that, having created this liberty interest, New York must provide appropriate due process. Although we recognized that only a minimum of process is due given the prison environment and the relatively minor deprivation of liberty occasioned by a transfer from the general prison population to administrative confinement, we concluded that the failure to afford the confined inmate an opportunity to make a written or oral statement to the officer in charge of his confinement rendered the New York scheme unconstitutional. Gittens, 891 F.2d at 40-41. Indeed, allowing the confined inmate to be heard on his administrative confinement only' at the disciplinary hearing on the underlying charges of misbehavior effectively precludes a challenge to the confinement itself. We also noted with approval in Gittens that New York regulations require appointment of a Review Officer to review misbehavior reports and the status of inmates in keeplock. N.Y.Comp.Code R. & Regs. tit. 7, § 251-2.2 (1992).
In this case, unlike Gittens, Shamsid-Deen was given an opportunity to write to a responsible official, Cunningham, who was the Acting Deputy Superintendent for Security.5 Indeed, Shamsid-Deen concedes that he submitted a written complaint to Cunningham asserting the impropriety of his administrative confinement, but he contends that he did not receive a response from Cunningham. Although we recognize that a response would have been thoughtful, due process does not require such a response. As the Supreme Court held in Hewitt, the process that is due to an inmate confined to keeplock is “an informal, non-adversary review of the information supporting [the inmate’s] administrative confinement, including whatever statement [the inmate] wished to submit, within a reasonable time after confining him to administrative segregation.” 459 U.S. at 472, 103 S.Ct. at 872 (emphasis added). In our view, mandating that prison officials issue a response under these circumstances would be tantamount to inferring that, where a response has not been issued, the responsible officials have not considered the complaint. In keeping with our traditional and well founded deference to prison officials in their administration of the prison, we refuse to draw such an inference in the absence of any other evidence that the confined inmate’s complaint has been ignored. Accordingly, we conclude that Shamsid-Deen’s opportunity to write to Cunningham afforded him a constitutionally adequate opportunity to be heard regarding his administrative confinement, and we therefore need not address the magistrate judge’s additional conclusion that the disciplinary hearing itself constituted an adequate opportunity to be heard.
We next consider the due process requirement that the opportunity to be heard occur within a reasonable time after the imposition of keeplock. Hewitt, 459 U.S. at 472, 103 S.Ct. at 871; Gittens, 891 F.2d at 41. Here, Shamsid-Deen himself acknowledges that he wrote to Cunningham on August 11, the day on which his administrative confinement commenced. This opportunity came within the reasonable time requirement.
Moreover, we are not persuaded by Sham-sid-Deen’s contention that Lieutenant Inser-ra failed to review Shamsid-Deen’s keeplock status pursuant to section 251-2.2. Sham-sid-Deen’s claim seems to be that, because Inserra did not order Shamsid-Deen’s release from prehearing keeplock, Inserra could not have performed his review duties adequately. This argument is circular and conclusory, and we therefore reject it.
Shamsid-Deen thus had an opportunity to be heard “at a meaningful time and in a meaningful manner,” Mathews v. Eldridge, 424 U.S. 319, 333, 96 S.Ct. 893, 902, 47 L.Ed.2d 18 (1976) (citation omitted), and “the opportunity to avoid an improvident or wrongful administrative confinement was [not] lost.” Gittens, 891 F.2d at 41. Accord[537]*537ingly, we conclude that Shamsid-Deen’s pre-hearing confinement satisfied procedural due process requirements.
2. Validity of Confinement
Shamsid-Deen also alleges that the defendants improperly and arbitrarily placed him in keeplock pending his disciplinary hearing, a claim rejected by the magistrate judge. We construe this contention as raising a substantive due process challenge, and we conclude that Shamsid-Deen’s administrative confinement did not violate his right to substantive due process.
Substantive due process protects individuals against government action that is arbitrary, Daniels v. Williams, 474 U.S. 327, 331, 106 S.Ct. 662, 665, 88 L.Ed.2d 662 (1986); United States v. Certain Real Property and Premises, 954 F.2d 29, 33 (2d Cir.), cert. denied, — U.S. -, 113 S.Ct. 55, 121 L.Ed.2d 24 (1992), conscience-shocking, Rochin v. California, 342 U.S. 165, 172, 72 S.Ct. 205, 209, 96 L.Ed. 183 (1952); Doherty v. Thornburgh, 943 F.2d 204, 209 (2d Cir.1991), cert. dismissed sub nom. Doherty v. Barr, — U.S. -, 112 S.Ct. 1254, 117 L.Ed.2d 485 (1992), or oppressive in a constitutional sense, DeShaney v. Winnebago County Dep’t of Social Services, 489 U.S. 189, 196, 109 S.Ct. 998, 1003, 103 L.Ed.2d 249 (1989); Interport Pilots Agency v. Sammis, 14 F.3d 133, 144 (2d Cir.1994), but not against government action that is “incorrect or ill-advised,” Bishop v. Wood, 426 U.S. 341, 350, 96 S.Ct. 2074, 2080, 48 L.Ed.2d 684 (1976); Interport Pilots, 14 F.3d at 144. Moreover, government action might be so arbitrary that it violates substantive due process “regardless of the fairness of the procedures used.” Foucha v. Louisiana, — U.S. -, -, 112 S.Ct. 1780, 1785, 118 L.Ed.2d 437 (1992); Daniels, 474 U.S. at 331, 106 S.Ct. at 665; Interport Pilots, 14 F.3d at 144.
The first step in substantive due process analysis is to identify the constitutional right at stake. See Collins v. City of Harker Heights, — U.S. -, -, 112 S.Ct. 1061, 1068, 117 L.Ed.2d 261 (1992). Here, the right allegedly violated was Sham-sid-Deen’s liberty interest in remaining free from administrative confinement unless a correction officer has reasonable grounds to believe that he poses a threat to the order, safety or security of the correctional facility. See N.Y.Comp.Code R. & Regs. tit. 7, § 251-1.6(a). •
Having identified the constitutional interest at stake, we must now consider whether the state action — administrative confinement — was arbitrary in the constitutional sense and therefore violative of substantive due process. One of the bases for Shamsid-Deen’s administrative confinement was his refusal to obey the direct order of a correction official in or near the mess hall, where inmates typically gather, during the evening meal service. Because this failure to comply with Achtyl’s demand occurred in the mess hall setting, it arguably created at least the potential for disruption of the order and security of the prison, regardless of Achtyl’s motivation for demanding that Shamsid-Deen give him the hot sauce. Indeed, even if Achtyl had acted on purely improper motives in demanding that Shamsid-Deen give him the hot sauce, Shamsid-Deen’s failure to comply with that demand arguably gave Achtyl reasonable grounds to believe that a threat to the prison’s order existed. Shamsid-Deen having thus created a threat to the security of the prison by refusing a direct order in a mess hall setting, his subsequent administrative confinement was not arbitrary or conscience-shocking in the constitutional sense.6 Accordingly, Shamsid-Deen’s administrative confinement did not violate substantive due process.
CONCLUSION
We have considered each of Shamsid-Deen’s claims and conclude that none is persuasive. Accordingly, we affirm.