
961 P.2d 1134 (1997)
DIAMOND BACK SERVICES, INC., a Colorado corporation, Plaintiff-Appellee,
v.
WILLOWBROOK WATER AND SANITATION DISTRICT, Defendant-Appellant.
No. 96CA0693.
Colorado Court of Appeals, Div. IV.
October 16, 1997.
Rehearing Denied December 18, 1997.
Certiorari Denied July 27, 1998.
*1135 Meer & Meer, P.C., Robert Meer, Denver, Dana F. Strout, P.C., Dana F. Strout, Camden, ME, for Plaintiff-Appellee.
Hall & Evans, L.L.C., Alan Epstein, Jeffery B. Stalder, Denver, for Defendant-Appellant.
Opinion by Judge KAPELKE.
Defendant, Willowbrook Water and Sanitation District, appeals from orders granting plaintiff, Diamond Back Services, Inc., relief from judgment pursuant to C.R.C.P. 60, and taxing costs of suit against Willowbrook. We affirm.
Diamond Back filed this action for wrongful termination and breach of a contract between it and Willowbrook for the construction of a sewer line. After a bench trial, the trial court entered judgment in favor of Diamond Back, finding that Willowbrook had wrongfully terminated the contract. The court awarded compensatory damages for extra work performed by Diamond Back before termination. However, the order did not address Diamond Back's claim for the balance due for work performed under the contract.
Both Diamond Back and Willowbrook timely filed motions to alter or amend the judgment pursuant to C.R.C.P. 59. In its motion, Diamond Back requested an amendment to include an award of damages for amounts unpaid on the contract. Willowbrook, in its motion, sought a setoff for expenses it claimed to have incurred in correcting Diamond Back's allegedly defective work.
Diamond Back also filed a motion to tax costs against Willowbrook. Willowbrook objected to the inclusion of certain costs relating to depositions, transcript preparation, and expert witnesses. However, Willowbrook did not argue before the trial court that, because it is a public entity, it is exempt from taxation of costs.
Sixty-eight days after Willowbrook's motion to alter or amend was filed, the court issued an order amending its judgment to include the unpaid balance owed Diamond Back on the contract, stating that the award of compensation on this claim had been "inadvertently omitted" from the original judgment. *1136 Willowbrook's motion for a setoff was denied. The court also granted, with some modifications, Diamond Back's motion for costs.
Willowbrook filed a notice of appeal forty days after the court issued its order on the post-trial motions. In an order to show cause, this court noted that the trial court had issued its order on the motions to alter or amend the judgment outside the sixty-day limit mandated by C.R.C.P. 59(j), that the trial court's order was therefore a nullity, and that Willowbrook's notice of appeal was filed well over forty-five days after the trial court's original judgment, thus rendering the appeal untimely under C.A.R. 4(a).
In response, Diamond Back initially agreed that the appeal was untimely and moved to dismiss it. Later, Diamond Back reversed its position and requested that, rather than dismissing the appeal outright, this court remand the matter to the trial court to allow Diamond Back an opportunity to move for relief from judgment pursuant to C.R.C.P. 60.
After reviewing the parties' responses, a division of this court determined that Willowbrook's appeal was untimely as to the award of damages but timely as to the taxation of costs against Willowbrook. The division also granted Diamond Back's request that the matter be remanded to the trial court to allow Diamond Back to file a motion for relief from judgment.
On remand, the trial court granted Diamond Back's motion for relief from judgment. The court found that its failure to include in the judgment the award of damages for the balance under the contract was a clerical error subject to correction under C.R.C.P. 60(a) in order to "speak the truth of the court's original intent." The court also found that extraordinary circumstances justified relief under C.R.C.P. 60(b)(5). Accordingly, the trial court reinstated the contract damage award. The matter was then recertified to this court.

I.
Willowbrook first contends that the trial court erred in granting Diamond Back relief from judgment under C.R.C.P. 60(a). Under the circumstances here, we disagree.

A.
C.R.C.P. 60(a) provides, in pertinent part:
Clerical mistakes in judgments, orders, or other parts of the record and errors therein arising from oversight or omission may be corrected by the court at any time of its own initiative or on the motion of any party and after such notice, if any, as the court orders. (emphasis added)
C.R.C.P. 60(a) can apply to errors or omissions by the trial court itself. Reasoner v. District Court, 197 Colo. 516, 594 P.2d 1060 (1979); McNeill v. Allen, 35 Colo. App. 317, 534 P.2d 813 (1975). However, relief under C.R.C.P. 60(a) is limited to cases in which the trial court originally intended to make the award granted by corrective amendment. See Jennings v. Ibarra, 921 P.2d 62 (Colo.App.1996) (postjudgment interest awarded under C.R.C.P. 60(a) because record showed that trial court intended it, but prejudgment interest denied because of failure to demonstrate that trial court originally intended such an award).
As has been said of Fed.R.Civ.P. 60(a), the federal counterpart of C.R.C.P. 60(a), the rule "is designed to strike a balance between rendering justice to the parties and ensuring that litigation ends within a finite period of time." 12 J. Moore, Moore's Federal Practice § 60.11[3] at 60-38 (3d ed.1997).
Here, the trial court's original judgment contained extensive findings that Willowbrook had wrongfully terminated its contract with Diamond Back. Although there was virtually no dispute as to the actual amount of the balance owing on the contract itself, the trial court omitted any mention of that component of the damage claim. Rather, the court's judgment focused entirely on Diamond Back's claims for extra work and alleged losses of future profits. In both the order amending the judgment and the order granting relief from judgment under C.R.C.P. 60, however, the court stated that it had originally intended to award Diamond *1137 Back damages for the unpaid balance owed for work performed under the contract but had inadvertently neglected to do so.
Thus, the record demonstrates that the trial court originally intended to grant the relief that was the subject of the amended judgment and that the omission of any mention of Diamond Back's claim for amounts due on the contract was the result of a judicial error correctable under the terms of C.R.C.P. 60(a). We therefore conclude that the court did not err in granting relief from the judgment.

B.
Willowbrook asserts that, in granting relief from the judgment, the trial court impermissibly allowed Diamond Back to circumvent the sixty-day limit specified in C.R.C.P. 59(j) for determination of motions to alter or amend judgments. We are unpersuaded.
It is true that a motion for relief from judgment under C.R.C.P. 60(b) may not be used to circumvent the sixty-day limit of C.R.C.P. 59(j) or as a substitute for appeal. Guevara v. Foxhoven, 928 P.2d 793 (Colo. App.1996). This principle is intended to protect the finality of judgments. Canton Oil Corp. v. District Court, 731 P.2d 687 (Colo. 1987).
A motion for relief from an error under C.R.C.P. 60(a), in contrast, may be filed at any time. Reasoner v. District Court, supra; In re Marriage of Cespedes, 895 P.2d 1172 (Colo.App.1995).
No time requirement is imposed for a C.R.C.P. 60(a) motion because the purpose of such a motion is limited to making the judgment speak the truth as originally intended and the correction does not entail a relitigation of matters which have already been decided. See 11 Charles Alan Wright, Arthur R. Miller & Mary Kay Kane, Federal Practice & Procedure § 2852 (1995) (construing counterpart Fed.R.Civ.P. 60(a)).
Here, Diamond Back first brought the trial court's omission to its attention in the form of a motion to alter or amend the judgment pursuant to C.R.C.P. 59. However, given the nature of the omission and the evidence in the record of the trial court's original intent, there was no need for relitigation of the merits of the dispute. Under these circumstances, the failure of the trial court to enter a timely ruling on the C.R.C.P. 59 motion did not bar the later motion under C.R.C.P. 60(a).

II.
Defendant next contends that the trial court lacked authority to tax costs against it because it is a public entity. We decline to address this contention.
In general, an appellate court may consider only issues that have actually been determined in the first instance by a trial court or agency. Committee for Better Health Care v. Meyer, 830 P.2d 884 (Colo. 1992). Contentions not raised in the trial court are not properly preserved for appellate review. Boyett v. Smith, 888 P.2d 294 (Colo.App.1994).
Here, as noted above, in the trial court Willowbrook did not assert its public entity status as a basis for exemption from costs. We reject its contention that it could not have presented such an objection in the trial court. Thus, the exemption issue is not properly before us and will not be considered.
The judgment is affirmed.
JONES and ROY, JJ., concur.
