David Wardle appeals the district court’s grant of summary judgment in favor of the Lexington-Fayette Urban County Government (“LFUCG” or the “government”) in his suit charging LFUCG with violating his Fourth, Fifth, and Fourteenth Amendment rights and various state laws. Wardle is an employee of LFUCG and his claims arise out of a drug and alcohol test he was forced to take after he was involved in a minor accident while driving a county vehicle. The district court considered the parties’ cross-motions for summary judgment and held that the government’s actions did not violate Wardle’s constitutional rights; having dismissed Wardle’s federal claims, the court declined to exercise jurisdiction over Wardle’s state law claims and dismissed those claims without prejudice. Because Wardle failed to raise the arguments he presents to this court before the district court, we affirm the district court’s disposition.

I

Wardle is employed by LFUCG as a carpenter in its Division of Building Maintenance and Construction. On April 28, 1999, Wardle backed the LFUCG vehicle he was driving into a pillar. Section XI(F) of LFUCG’s “Alcohol and Drug Free Workplace Policy,” entitled “PosWCritical Incident Testing (PCI),” requires employees involved in a single vehicle accident involving property damage of $2,500 or more to notify their supervisor immediately and take a drug and alcohol test.

Wardle notified his supervisor, Ben Turpin, who in turn notified his superior, Carolyn Smith, director of the Division of Building Maintenance and Construction. Smith instructed Turpin to have Wardle take a drug test. Wardle argued unsuccessfully that a drug test was not called for, because the damage was sure to be less than $2,500. Both Wardle and Turpin stated in deposition testimony that Turpin expressed to Smith no opinion as to the level of damage and told Wardle that he could not estimate the amount of damage.

Turpin accompanied Wardle that day to an independent medical facility called an Urgent Treatment Center (“UTC”), where Wardle took a drug and alcohol test. On May 4, 1999, the UTC informed LFUCG that Wardle had tested positive for drugs. Based on that result, LFUCG suspended Wardle for thirty days and ordered him to submit to a substance abuse evaluation. However, Susie Taylor, a member of the LFUCG human resources department who oversees the drug testing program, testified that she learned on May 5, 1999 that it had been determined that Wardle’s accident had caused less than $2,500 in damage and therefore did not invoke a mandatory drug test. Wardle’s suspension was immediately revoked, all record of his posi*507tive test was removed from his personnel file, and he was reinstated with back pay.

Wardle filed suit in district court, alleging that the testing violated his Fourth and Fifth Amendment rights as applied to the state by the Fourteenth Amendment. He also alleged violations of corresponding provisions of the Kentucky Constitution, and he asserted state law claims for breach of contract, breach of an implied covenant of good faith and fair dealing, intentional infliction of emotional distress, fraud, deceit, and misrepresentation. After the government’s answer, Wardle moved for partial summary judgment on his Fourth Amendment claim. The government moved for summary judgment on all of Wardle’s claims.

In deciding the summary judgment cross-motions before it, the district court addressed Wardle’s argument that “requiring him to undergo drug and alcohol testing when the property damage fell below the threshold set forth in the LFUCG’s ‘Alcohol and Drug Free Workplace Guidelines and Procedures’ eonsti-tute[d] an unreasonable search in violation of the Fourth Amendment.”1 It is important to note, however, that Wardle did not contest LFUCG’s assertion that it discovered that the accident had caused less than $2,500 damage after it received the positive test result and suspended Wardle.2 Accordingly, the district court understandably read Wardle’s complaint as alleging that LFUCG violated Wardle’s constitutional rights by testing him in what it later found out to have been contravention of its drug testing policy.

The court first noted that drug testing required by a government employer is considered a search, that a search must be reasonable to avoid running afoul of the Fourth Amendment, and that a search generally must be based on individualized suspicion for it to be reasonable. See Skinner v. Ry. Labor Executives’ Ass’n, 489 U.S. 602, 618-20, 109 S.Ct. 1402, 103 L.Ed.2d 639 (1989). However, the court went on to note that there is an exception to the individualized suspicion rule, under which a search can be reasonable based upon “special needs” of the government; in evaluating the constitutionality of a search premised on special needs, the district court wrote that it must balance the privacy interest of the plaintiff against the government’s interest in the search. See id. at 619.

In conducting this balancing, the court first held that Wardle’s privacy interest was diminished by the fact that he knew in advance that he could be tested following a single vehicle accident. While it was true that the damage turned out to be below the $2,500 threshold, the court explained that LFUCG did not know that at the time *508of the test; it was therefore necessary for LFUCG to test Wardle, both because the Handbook required testing within eight hours and because drugs pass from the system with time. The court finally mentioned that the drug testing was accomplished with a minimum of intrusiveness, as it was done at an independent medical center and Wardle had not alleged that he was observed in any way during the test.

The court held that the burden placed on Wardle’s diminished expectation of privacy was outweighed in this case by LFUCG’s interests in protecting public safety by keeping impaired drivers off the road, deterring drug use among employees, and determining the cause of the accident. Therefore, the court held that the testing was reasonable for Fourth Amendment purposes and granted LFUCG’s motion for summary judgment on Wardle’s constitutional claims. The court then dismissed without prejudice Wardle’s state law claims. Wardle filed an unsuccessful motion for reconsideration and then appealed the district court’s grant of summary judgment to this court.

On appeal, Wardle argues that the district court erred in two ways in granting LFUCG’s summary judgment motion. First, Wardle contends that the court ignored a “judicial admission” by LFUCG that Wardle had been tested in contravention of its drug testing policy, thereby making the testing unreasonable per se. Second, Wardle argues that the court erred in failing to recognize that, regardless of whether the testing was performed in contravention of LFUCG’s policy, the testing violated Wardle’s Fourth Amendment right to be free from unreasonable searches. According to Wardle, for a governmental employer’s post-accident drug testing to pass constitutional muster, the target employee must be engaged in safety-sensitive activities; Wardle contends that his job is not safety sensitive.

LFUCG’s Admission

In its answer to Wardle’s complaint, LFUCG admitted that “an error was made in requesting Wardle to undergo a test when the actual property damage done to the vehicle was less than $2,500.” Answer at 3. Wardle argues on appeal that “for suspicionless post-accident drug-testing to be appropriate, the government is required to implement a minimum threshold of damage [and to] follow that policy without discretion .... ” Appellant’s Brief at 16. He contends that LFUCG’s admission shows that it ordered him tested knowing that the vehicle damage did not meet the drug policy threshold, and that this makes the drug testing Wardle was forced to undergo unreasonable and therefore viola-tive of his Fourth Amendment rights.

There is a strong argument, based on the Supreme Court’s decision in Skinner v. Railway Labor Executives’ Association, 489 U.S. 602, 109 S.Ct. 1402, 103 L.Ed.2d 639 (1989), that if the government knew the damage did not meet the threshold for drug testing set out in its guidelines, the resultant test would violate Wardle’s Fourth Amendment rights. In Skinner, the Court determined that a government policy requiring drug and alcohol testing after major railroad accidents did not violate the employees’ Fourth Amendment rights because the government’s interest in the testing outweighed the employees’ privacy rights. See id. at 618-20. Specifically, the Court noted that testing can be valid “[i]n limited circumstances, where the privacy interests implicated by the search are minimal, and where an important governmental interest furthered by the intrusion would be placed in jeopardy by a requirement of individualized suspicion ....” Id. at 624. If it were clear to *509all involved that the accident did not meet the threshold requirement for drug testing, then Wardle’s expectation of privacy would be significantly greater and the governmental interest in testing would be significantly less than if it were unclear whether the accident qualified for the mandatory drug testing.

However, contrary to Wardle’s assertion on appeal, LFUCG’s “judicial admission” was not necessarily an admission that the drug test Wardle was forced to take contravened LFUCG’s drug testing policy. Indeed, it appears that the district court read the admission as meaning that, at the time of the testing, LFUCG did not know whether the accident damage met the threshold but it later became clear that it did not. With this apparent understanding, the court held that it was reasonable for LFUCG to require the test and then withdraw its effects as soon as the LFUCG managers found out that the damage did not meet the threshold. Obviously, the distinction comes down to when LFUCG can be credited with knowing that the damage was less than $2,500.

In his complaint, Wardle alleged generally that LFUCG failed to follow its guidelines because he was forced to undergo a drug test and the damage turned out not to meet the $2,500 threshold. In its motion for summary judgment, LFUCG stated that at the time of testing, it did not know whether the damage would turn out to meet the threshold, so it ordered the test. LFUCG explained that it did not find out that the damage did not meet the threshold until after it received the results of the test. In his response to LFUCG’s motion, Wardle did not contest this statement, and the district court adopted it as an undisputed fact.

In his post-summary judgment motion to vacate, Wardle argued for the first time that LFUCG knew that the damage did not meet the threshold level at the time it ordered the test. On appeal, Wardle argues that LFUCG knew the damage was insufficient on the day of the accident, or at the very least, the day after it ordered the test (before the results were received). He cites as evidence the incident report filled out by Turpin on the day of the accident and the three auto body shop estimates received by LFUCG the day after the accident.

If Wardle had pointed out this question of fact in his response to the government’s motion for summary judgment, then it is clear that the district court would have been required to assume Wardle’s view of the facts for the purpose of deciding the government’s motion. See Matsushita Elec. Indus. Co. v. Zenith Radio Corp., 475 U.S. 574, 587-88, 106 S.Ct. 1348, 89 L.Ed.2d 538 (1986) (noting that at the summary judgment stage, evidence and facts must be viewed in the light most favorable to the non-movant). Either of these likely would have made summary judgment inappropriate.

However, a district court is not required to search the record to determine whether genuine issues of material fact exist when the non-moving party has failed to point them out. See Street v. J.C. Bradford & Co., 886 F.2d 1472, 1479-80 (6th Cir. 1989) (“The trial court no longer has the duty to search the entire record to establish that it is bereft of a genuine issue of material fact.”). Instead, when the non-movant has failed to point out a question of fact on an issue, a district court’s “reliance on the facts advanced by the movant is proper and sufficient.” Guarino v. Brookfield Township Trustees, 980 F.2d 399, 404 (6th Cir. 1992) (in the context of an unopposed summary judgment motion).

It is true that Wardle pointed out this question of fact in his post-judgment “Mo*510tion to Alter, Vacate, or Amend.” However, motions to alter or amend judgment are properly used to point out clear errors of law, newly discovered evidence, or an intervening change in controlling law, or to prevent manifest injustice. See GenCorp, Inc. v. Am. Int’l Underwriters, 178 F.3d 804, 834 (6th Cir. 1999). Since there is no contention that any of these applies to excuse Wardle’s failure to raise timely the question of fact as to when LFUCG knew the value of the vehicle damage, the fact that Wardle raised it in his post-judgment motion for reconsideration does not help him. Accordingly, we find no error in the district court’s acceptance of LFUCG’s version of the facts and the interpretation of LFUCG’s admission that followed therefrom.

Wardle’s Challenge to the Constitutionality of LFUCG’s Drug Testing Policy

Wardle’s central argument on appeal, though stated in different ways throughout his brief, is that LFUCG could not have forced him to take a post-accident drug test without violating his Fourth Amendment rights, no matter what the degree of damage in the accident, because his job does not require him to engage in “safety-sensitive activities involving passengers or hazardous materials.” Appellant’s Brief at 18. Essentially, Wardle argues that case law supports a legal distinction between employees whose jobs are “fraught with danger” and therefore implicate “strong safety interests,” and those whose jobs do not. Id. at 21. According to Wardle’s argument, post-accident testing of the former can be reasonable, and thus constitutionally permissible; however, testing of the latter can not be reasonable. Wardle, who professes to be “nothing more than a basic carpenter engaged in routine repair work, who simply happens to drive an LFUCG vehicle to and from job sites from time to time,” contends that he falls into the category of employees not engaged in safety-sensitive activities. According to Wardle, the district court erred in failing to recognize both this distinction and its application to this case, and the court therefore erred in its determination that LFUCG’s post-accident drug testing of Wardle was reasonable.

Wardle’s argument — that post-accident drug testing applied to him is per se unreasonable because he is not engaged in safety-sensitive tasks — is best read as a challenge to the constitutionality of LFUCG’s policy itself. The problem with this argument is that Wardle never made it before the district court prior to the court’s disposition of the case. He did not challenge the constitutionality of LFUCG’s drug testing policy on the basis that it failed to take into account the nature of his job in his complaint, his summary judgment motion, or his memorandum in opposition to the government’s summary judgment motion. This argument appears for the first time in Wardle’s motion to vacate the district court’s summary judgment order.

As mentioned above, Wardle argued in his pre-judgment filings only that LFUCG violated his constitutional rights by failing to follow its drug testing policy guidelines. See, e.g. Complaint at 3 (“Despite the clear limitation contained in the Post Critical [Incident] Testing provisions of the Handbook, the LFUCG elected to ignore these Fourth Amendment protections and immediately required Wardle to undergo an illegal search.... ”); Complaint at 5 (“By failing to follow its written procedure for drug testing, the LFUCG willfully and intentionally violated the minimum standards of adequate notice and legal justification of the U.S. Constitution ....”); Memorandum in Opposition at 7 (“the PCI test to which the LFUCG subjected [Wardle] is unconstitutional because, inter alia, it did not comport with the guidelines provided *511by the Handbook”). Indeed, before the district court, Wardle expressly disavowed any argument that the drag testing policy itself was unconstitutional:

Plaintiff has never seriously argued that the Handbook provisions governing PCI testing are unconstitutional because, in this case, the LFUCG has unequivocally admitted that the test was administered outside of the parameters of its own handbook (and thus, outside of the parameters of the Constitution).

Memorandum in Opposition at 7. It is therefore clear that Wardle did not challenge the constitutionality of LFUCG’s drug testing policy before the district court pre-judgment.

This court does not ordinarily address new arguments raised for the first time on appeal. See GenCorp, 178 F.3d at 817; Elkins v. Richardson-Merrell, Inc., 8 F.3d 1068, 1072 (6th Cir. 1993) (noting that this court will not normally address issues raised for the first time on appeal). In explaining why, this court has written:

“Propounding new arguments on appeal in attempting to prompt us to reverse the trial court — arguments never considered by the trial court — is not only somewhat devious, it undermines important judicial values.... In order to preserve the integrity of the appellate structure, we should not be considered a ‘second shot’ forum, a forum where secondary, back-up theories may be minted for the first time.”

Isaak v. Trumbull S & L Co., 169 F.3d 390, 396 n. 3 (6th Cir. 1999) (quoting Estate of Quirk v. Commissioner of Internal Revenue, 928 F.2d 751, 758 (6th Cir. 1991)).

Furthermore, just as it did not help Wardle to have challenged LFUCG’s version of the facts for the first time in his post-judgment motion to alter, the fact that Wardle challenged the constitutionality of LFUCG’s policy in the same motion does not change this analysis. Wardle’s motion for reconsideration was pursuant to Federal Rule of Civil Procedure 59(e). “Rule 59(e) motions are aimed at reconsideration, not initial consideration. Thus, parties should not use them to raise arguments which could, and should, have been made before judgment issued.” Sault Ste. Marie Tribe of Chippewa Indians v. Engler, 146 F.3d 367, 374 (6th Cir. 1998) (quoting FDIC v. World Univ. Inc., 978 F.2d 10, 16 (1st Cir. 1992) (internal quotations and citations omitted)); see also Zimmerman v. City of Oakland, 255 F.3d 734, 740 (9th Cir. 2001) (“A district court does not abuse its discretion when it disregards legal arguments made for the first time on a motion to amend”); Pacific Ins. Co. v. Am. Nat'l Fire Ins. Co., 148 F.3d 396, 404 (4th. Cir. 1998) (“a party should not be permitted to raise new arguments or legal theories of liability on a motion to alter or amend the judgment under Rule 59(e)”).

Since Wardle never argued before the district court that LFUCG’s drug testing policy was unconstitutional because it failed to take into account the nature of his job, we find no error in the district court’s failure to consider this argument and deem it waived on appeal.

Ill

For the foregoing reasons, we AFFIRM the district court’s grant of summary judgment in favor of LFUCG.