In this appeal, we review the district court’s denial of a Motion to Alter or Amend Judgment pursuant to Federal Rule of Civil Procedure 59(e). This is a run of the mill political discrimination case brought against appellants, Municipality of Luquillo, Puerto Rico and several officials of the Municipality, under 42 U.S.C. § 1983 for violation of appel-lees’ First Amendment rights under the United States Constitution. The jury found that the appellants discriminated against ap-pellees, thirty-eight former employees of the Municipality, and awarded damages in favor of twenty-seven appellees. Appellants request that we vacate the judgment of the district court entirely because the evidence was insufficient to support the jury’s verdict that appellants terminated appellees because of their political affiliation. Alternatively, appellants pray that we reduce the damage awards because they are allegedly excessive. Plaintiff-appellees, in a cross-appeal, request that they be reinstated in their employment.

I

Normally, to challenge the sufficiency of the evidence on appeal, a party must move for a directed verdict at the close of all the evidence and follow it by a motion for judg[*427] ment notwithstanding the verdict. See Fed. R.Civ.P. 50(a) & (b); Wells Real Estate, Inc. v. Greater Lowell Board of Realtors, 850 F.2d 803, 810 (1st Cir.), cert. denied, 488 U.S. 955, 109 S.Ct. 392, 102 L.Ed.2d 381 (1988). Motions for directed verdict and judgment n.o.v. must be made with sufficient particularity to alert the trial judge as to why the evidence is insufficient. The moving party may appeal only from the grounds stated in the motion. Id.; Pstragowski v. Metropolitan Life Ins. Co., 553 F.2d 1, 3 (1st Cir.1977). Since appellants failed to move for a directed verdict and judgment n.o.v., we may not consider this ground of appeal. Wells Real Estate, 850 F.2d at 810; La Forest v. Autoridad de las Fuentes Fluviales, 536 F.2d 443, 445 (1st Cir.1976).

However, waiver of the right to request a judgment n.o.v. does not prevent a party from moving for a new trial under Fed.R.Civ.P. 59(a), alleging that the verdict is against the weight of the evidence. Wells Real Estate, 850 F.2d at 810. “[A] motion for a new trial must be made in the first instance before the trial court, particularly where the weight of the evidence is at issue.” Id., 850 F.2d at 811 (citing 6A James WM. Moore, Moore’s Federal Practice § 59.15[3], at 326-27 (2d ed. 1987)). Failure to move for a new trial also waives the issue on appeal. Id.

In this case, appellants once again failed to make an appropriate motion for a new ti’ial before the district court. Instead, they moved under Fed.R.Civ.P. 59(e) to set aside or amend the verdict. ^[1] The purpose of the motion, however, was indisputably to challenge the verdict as against the weight of the evidence. While we do not condone lax, self-styled motions, or disregard of the Rules, our examination of the character of a motion is functional: “nomenclature should not be exalted over substance.” Echevama-González v. González-Chapel, 849 F.2d 24, 26 (1st Cir.1988) (quoting Lyell Theatre Corp. v. Loews Corp., 682 F.2d 37, 41 (2d Cir.1982)). We therefore cannot conclude that appellants failed to raise the issue before the district court.

The district court apparently did not pay much attention to the rule under which the motion was filed, or the caption that titled appellants’ plea. The magistrate judge addressed the sufficiency argument directly and denied appellants’ motion because he believed that “[t]hejury received abundant testimonial and documentary evidence with which to support their conclusion of political discrimination.” Rosa-Velázquez v. Figueroa-Gómez, No. 90-1192, slip op. at 1 (D.P.R. Apr. 15,1992). In addition, appellees did not object to the styling of the motion and seemed to assume that sufficiency of the evidence could be assailed in a motion under Rule 59(e). Thus, while the district court ought to have reformed the challenge as one pursuant to Rule 59(a) earlier in this proceeding, we will treat the motion as one for a new trial.

The decision to grant a new trial is squarely within the trial court’s discretion. Allied Chemical Corp. v. Daiflon, Inc., 449 U.S. 33, 36, 101 S.Ct. 188, 190-91, 66 L.Ed.2d 193 (1980). “Only an abuse of discretion will trigger reversal of a denial of a motion for new trial.” Wells Real Estate, 850 F.2d at 811; see also Conway v. Electro Switch Corp., 825 F.2d 593, 598 (1st Cir.1987). Such deference to the trial court is particularly appropriate in cases in which the jury’s verdict is challenged as against the weight of the evidence because “a jury’s verdict on the facts should only be overturned in the most compelling circumstances.” Wells Real Estate, 850 F.2d at 811; Keeler v. Hewitt, 697 F.2d 8, 11 (1st Cir.1982).

[*428] Moreover, the trial court’s discretion is quite limited concerning motions for new trials. A trial judge may not upset the jury’s verdict merely because he or she might have decided the .case differently. On the contrary, a trial judge may grant a new trial only if she “believes that the outcome is against the clear weight of the evidence such that upholding the verdict will result in a miscarriage of justice.” Conway, 825 F.2d at 598-99; see also Coffran v. Hitchcock Clinic, Inc., 683 F.2d 5, 6 (1st Cir.), cert. denied, 459 U.S. 1087, 103 S.Ct. 571, 74 L.Ed.2d 933 (1982). We assume, and we do not review for, sufficiency of the evidence. Valm v. Hercules Fish Products, Inc., 701 F.2d 235 (1st Cir.1983).

We thus review the evidence to determine whether the district court abused its discretion. The evidence showed that all the plaintiffs were members of the Popular Democratic Party (“PDP”); that all defendants were members of the New Progressive Party (“NPP”); that many of the plaintiffs were politically active for the PDP during the 1988 campaign which brought the NPP to power; that defendants knew of the plaintiffs’ political affiliation prior to termination; that plaintiffs’ work responsibilities were altered with the change in administration; and that plaintiffs’ positions in the Municipal government were filled with members of the NPP after termination. Given this evidence, the district court did not abuse its discretion in finding the evidence sufficient to support the jury’s verdict and denying appellants’ motion.

II

Appellants’ second argument fails for similar reasons. Appellants urge that if the evidence is deemed sufficient, the damage awards be reduced because they are excessive. The standard of review of damage awards places an enormous burden on the party challenging the award. To begin with, the evidence is viewed in the light most favorable to the prevailing party. See, e.g., Betancourt v. J.C. Penney Co., 554 F.2d 1206, 1207 (1st Cir.1977). In addition, it is exceedingly “difficult on the basis of an algid appellate record to quantify damages for intangible losses.” Ruiz v. González-Caraballo, 929 F.2d 31, 34 (1st Cir.1991). Indeed, “[translating legal damage into money damages- — especially in cases which involve few significant items of measurable economic loss — is a -matter peculiarly within a jury’s ken.” Wagenmann v. Adams, 829 F.2d 196, 215 (1st Cir.1987). Therefore, unless we can say that the award is “‘grossly excessive,’ ‘inordinate,’ ‘shocking to the conscience of the court,’ or ‘so high that it would be a denial of justice to permit it to stand,’ ” Segal v. Gilbert Color Systems, Inc., 746 F.2d 78, 80-81 (1st Cir.1984) (quoting Grunenthal v. Long Island R.R. Co., 393 U.S. 156, 159 & n. 4, 89 S.Ct. 331, 333 & n. 4, 21 L.Ed.2d 309 (1968)), we will not “overrule a trial judge’s considered refusal to tamper with the damages assessed by a jury.” Ruiz, 929 F.2d at 34; see also Wagenmann, 829 F.2d at 215. We certainly cannot say that these awards for political discrimination in employment fall outside this broad standard for acceptable jury verdicts. ^[2]

Ill

The last issue that we must confront is whether the district court properly denied plaintiffs’ request for reinstatement. This Circuit has determined previously that “[o]ne of the remedies available for a political discharge in violation of First Amendment rights is reappointment.” Santiago-Negrón v. Castro-Dávila, 865 F.2d 431, 437 (1st Cir.1989). As reinstatement is an equitable remedy, we have stressed that its flexible application “seems particularly desirable in cases involving important private rights and public institutions” such as those involving political discrimination. Rosario-Torres v. Hernández-Colón, 889 F.2d 314, 320-21 (1st Cir.1989). We have rejected the notion that finding a violation of first amendment rights leads a fortiori to reinstatement, and recognized that the application of the remedy lies within the district court’s discretion. Id. at 321-22. The court must apply that discretion on a case by case basis with a keen eye to the many factors in the balance.

[*429] The trial court’s discretion is not unbounded, however. In fact, we have cautioned that the incidental burdens on a public employer accompanying reinstatement — i.e., “tension (or even hostility) between parties when forcibly reunited” — are “usually insufficient, without more,, to tip the scales against reinstatement when first amendment rights are at stake in a section 1983 action.” Id. at 322 (citing Banks v. Burkich, 788 F.2d 1161, 1165 (6th Cir.1986)). Thus, “equitable considerations different in kind or degree from those regularly accompanying reinstatement must be present if reinstatement is to be withheld from the victim of a first amendment infraction.” Rosario-Torres, 889 F.2d at 323.

In the past, we have indicated a number of special considerations that influence the district court determination in specific cases, including: (1) the strength of the evidence proving the first amendment violation; (2) whether the discharged employee has found comparable work; (3) the absence of a property right in the position because the employee was hired in violation of local law; and (4) the ineligibility of the employee for the position, due to failure to meet established qualifications, which would permit immediate discharge for no reason or for any permissible reason. See Hiraldo-Cancel v. Aponte, 925 F.2d 10, 13-14 (1st Cir.), cert. denied, — U.S. -, 112 S.Ct. 637, 116 L.Ed.2d 655 (1991); Rosario-Torres, 889 F.2d at 322-24. Although ineligibility for appointment “neither suspend[s] their first amendment rights nor undercuts] their entitlement to legal relief under section 1983,” it is a factor weighing against reinstatement if a reappointee would be immediately discharged. Hiraldo-Cancel, 925 F.2d at 14. While this list does not canvass all the relevant factors, it highlights several that are particularly important. With these principles in mind, we review the choice of equitable remedies for abuse of discretion while recognizing that the trial court views the evidence from a better vantage point than we do on the appellate record. Id.

In this ease the trial court denied reinstatement to all prevailing plaintiffs. The scant evidence supporting the first amendment claims, the amount of the damage awards, and the fact that these employees were hired illegally in violation of Puerto Rico’s personnel laws provided sufficient justification for denying reinstatement. We readily find no abuse of discretion.

IV

In conclusion, we affirm the trial court’s denial of the Rule 59(e) motion and plaintiffs’ request for reinstatement.