After examining the briefs and the appellate record, this three-judge panel has determined unanimously that oral argument would not be of material assistance in the determination of this appeal. See Fed.R. App.P. 34(a); Tenth Cir.R. 10(e). The cause is therefore ordered submitted without oral argument.
This appeal arises from an action in which the plaintiffs, Fred Vreeken and Kurt Vreeken, sought injunctive relief and damages from Internal Revenue Service agent Kent Davis, post office superintendent Lyle Stocks, and five John Doe defend*345ants, for injuries arising from the placement of a “mail cover”1 on the plaintiffs’ mail. Essentially, the plaintiffs alleged that the defendants violated the law and regulations governing the postal service in securing and maintaining the mail cover and that, in any event, the mail cover violated the plaintiffs’ Fourth Amendment rights. After a hearing the district court declared that it was granting summary judgment for the defendants on all claims and asked counsel to prepare and submit a suggested order. Before the court entered its written order, the plaintiffs filed a motion for leave to file a second amended complaint. The court denied the motion, treating it as a motion for relief from judgment under Fed.R.Civ.P. 60(b).
The issues on appeal are (1) whether the plaintiffs’ appeal was timely filed to permit appellate treatment of issues decided by the summary judgment; (2) whether the district court erred in granting summary judgment for the defendants; and (3) whether the district court properly denied the plaintiffs’ motion for leave to file a second amended complaint.
I
We first address the question of whether the plaintiffs’ appeal was timely as to the district court’s order of summary judgment. A party must file its notice of appeal within 30 days after entry of the judgment or order from which it appeals. Fed.R.App.P. 4(a). In the instant case, the district court stated in open court on March 16, 1982, that it would grant the defendants’ motion for summary judgment; it then entered the summary judgment order on March 30, 1982. In the interim, on March 23, the plaintiffs filed a pleading styled “Motion for Leave to File a Second Amended Complaint,” which the court denied on May 28, 1982. On June 25, 1982, the plaintiffs filed a notice of appeal. Thus, unless the plaintiffs’ motion of March 23 tolled the running of the time for filing a notice of appeal on the summary judgment order, the plaintiffs’ notice of appeal was untimely except as to the denial of the motion to file an amended complaint.
The defendants contend that the March 28 motion was a motion for relief from judgment pursuant to Fed.R.Civ.P. 60(b). At the hearing on the motion, counsel for the plaintiffs implied that he wished the district court to treat the motion as one made pursuant to Rule 60(b), and the court treated it as such. Thus, since the filing of a Rule 60(b) motion does not toll the running of the 30-day appeal period, Barta v. Long, 670 F.2d 907, 909 (10th Cir.1982), the defendants argue that appellate review in the instant case is limited to the district court’s denial of the plaintiffs’ Rule 60(b) motion.
We conclude, however, that the plaintiffs’ motion of March 23 is properly construed as a motion to alter or amend the judgment pursuant to Fed.R.Civ.P. 59(e). Generally, regardless of how it is styled or construed by the trial court, a motion filed within ten days of the entry of judgment that questions the correctness of the judgment is properly treated as a Rule 59(e) motion. Miller v. Leavenworth-Jefferson Electric Cooperative, Inc., 653 F.2d 1378, 1380 (10th Cir.1981). Although styled as a motion for leave to file an amended complaint, the March 23 motion also contains the request that the district court treat the motion as one made pursuant to Rule 52(b) or Rule 59 for purposes of the appeal time requirements of Fed.R.App.P. 4. Furthermore, at the hearing counsel for the plaintiffs asked the district court to construe the motion as one to set aside the order of summary judgment. A motion to vacate a *346judgment may constitute a motion to “alter or amend” the judgment within the meaning of Rule 59(e). Miller v. Leavenworth-Jefferson Electric Cooperative, Inc., 653 F.2d at 1380. A timely Rule 59(e) motion tolls the time for appeal until the district court rules on the motion, Fed.R.App.P. 4(a). We hold that the plaintiffs’ notice of appeal filed on June 25 was timely to permit plaintiffs to challenge on appeal all rulings of the district court.
II
Government officials imposed a mail cover on the plaintiffs’ mail on October 6,1981. The mail cover authorization required defendant Stocks to record the following information appearing on the outside cover of the plaintiffs’ incoming first-class mail: the addressee’s name, the sender’s name, the sender’s return address, the city and date of postmark, and the class of mail. The plaintiffs’ contentions are not entirely clear but apparently are that the district court erred in granting summary judgment for the defendants for three reasons: (1) government officials failed to comply with pertinent postal regulations in securing the mail cover; (2) a genuine issue of material facts exists as to whether the defendants and other individuals complied with the relevant postal regulations in conducting the mail cover; and (3) in any event, the mail cover violated the plaintiffs’ Fourth Amendment rights.
The postal regulation governing mail covers permits the Postal Inspector in Charge or his designee to order a mail cover when
“written request is received from any law enforcement agency of the Federal, State, or local governments, wherein the requesting authority stipulates and specifies the reasonable grounds that exist which demonstrate the mail cover would aid in the location of a fugitive, or that it would assist in obtaining information concerning the commission or attempted commission of a crime.”2
39 C.F.R. § 233.2(e)(l)(ii). The plaintiffs were under investigation by the Federal Grand Jury for the District of Utah. In connection with that investigation, Stewart C. Walz, an Assistant United States Attorney for the District of Utah, sent a letter to B. M. McClanahan, Postal Inspector in Charge, requesting that a mail cover be placed on one of the plaintiffs’ post office boxes. The letter stated, in relevant part,
“Fred and Kurt Vreeken are currently under investigation for allegedly providing fraudulent tax losses to hundreds of investors during 1977,1978,1979 and 1980 in violation of Title 26, Internal Revenue Code, Section 7206(2). The violation is a felony which provides for a maximum fine of $5,000 or imprisonment for not more than three (3) years, or both, together with costs of prosecution. Fraud by Wire and Mail Fraud may also be charged in the case ....
“Because the Vreekens deal with promoters or finders all over the country, it is necessary to employ a mail cover to identify these people along with the investors involved in the alleged scheme.”
R. I, 85-86. McClanahan’s designee, Assistant Postal Inspector in Charge Mclntire, authorized the mail cover on October 6, 1981. Later, the mail cover was extended to two other post office boxes used by the plaintiffs.
The plaintiffs contend that the letter failed to specify reasonable grounds demonstrating that the mail cover was necessary to obtain information regarding the commission of a crime, as required by 39 C. F.R. § 233.2. We disagree. In the instant case, the letter requesting the mail cover stated that the plaintiffs were the subjects of a grand jury investigation for tax fraud; it also specified why the mail cover was necessary to the investigation. The regulations do not require that the requesting agency state the factual predicate upon which it concludes that the subject of the mail cover is involved in the *347commission of a crime. United States v. Choate, 576 F.2d 165, 172 (9th Cir.), cert. denied, 439 U.S. 953, 99 S.Ct. 350, 58 L.Ed.2d 344 (1978). The letter requesting the mail cover complied with 39 C.F.R. § 233.2(e)(1)(ii).
In the alternative, the plaintiffs contend that summary judgment was improper because genuine issues of material fact exist regarding postal officials’ compliance with the postal regulations regarding their handling of the mail cover. Apparently, the plaintiffs assert that it is unclear whether defendant Stocks refrained from examining the contents of first-class mail, as contemplated by 39 C.F.R. § 233.2(c)(1). The plaintiffs question whether the mail cover excluded correspondence between the plaintiffs and their attorney, as required by 39 C.F.R. § 233.2(f)(2).
The party moving for summary judgment has the burden of establishing the absence of any genuine issue of material fact. Adickes v. S.H. Kress & Co., 398 U.S. 144,157,90 S.Ct. 1598,1608, 26 L.Ed.2d 142 (1970). When the moving party provides affidavits or other evidence that appear to meet this burden, the adverse party may not rest upon the mere allegations in his pleadings. Rather, he must submit affidavits or other evidence setting forth specific facts showing that there is a genuine issue for trial. Id. at 160; Fed.R.Civ.P. 56(e). In the instant case, the defendants supported their motion for summary judgment with a series of affidavits indicating that post office officials complied with all of the relevant regulations in conducting the mail cover. The plaintiffs failed to submit any affidavits in response. They had responses to interrogatories and had taken the depositions of both named defendants and two others. These items in the record fail to reveal any factual basis for the plaintiffs’ claims of procedural improprieties. Under these circumstances, summary judgment is appropriate. Baum v. Gillman, 648 F.2d 1292 (10th Cir.1981).
Finally, the plaintiffs assert that the mail cover violated their Fourth Amendment rights. A Fourth Amendment “search” occurs only when the government intrudes upon an individual’s reasonable expectations of privacy. Katz v. United States, 389 U.S. 347, 360, 88 S.Ct. 507, 516,19 L.Ed. 2d 576 (1967) (Harlan, J., concurring). Although the Supreme Court has not addressed directly the issue of the constitutionality of mail covers, its decision in Smith v. Maryland, 442 U.S. 735, 99 S.Ct. 2577, 61 L.Ed.2d 220 (1979), compels us to conclude that the mail cover does not violate the plaintiffs’ Fourth Amendment rights. In Smith the issue was whether the use of a pen register constitutes a “search” within the meaning of the Fourth Amendment. A pen register is a mechanical device that records the numbers dialed on a telephone but does not monitor the contents of the oral communications. The Court identified a two-fold inquiry for determining whether a person has a reasonable expectation of privacy within the meaning of Katz. First, the individual, by his conduct, must exhibit an actual or subjective expectation of privacy. Second, the individual’s subjective expectation of privacy must be one that is objectively reasonable or justifiable under the circumstances. 442 U.S. at 740, 99 S.Ct. at 2580. Applying these tests to the facts, the Supreme Court concluded that an individual has no reasonable expectation of privacy regarding the numbers he dials on his telephone. It emphasized that a telephone user typically knows that he must convey telephone numbers to the phone company when he uses a telephone. Thus, it is unlikely that a user would harbor a subjective expectation that the numbers dialed would remain private. Moreover, even if the subject harbors an actual expectation of privacy, that expectation is not objectively reasonable. An individual “has no legitimate expectation of privacy in information he voluntarily turns over to third parties.” Id. at 743-44, 99 S.Ct. at 2581-82. Thus, the Court concluded that the use of a pen register does not constitute a “search” for the purposes of the Fourth Amendment.
In our view, the mail cover at issue in the instant case is indistinguishable in any important respect from the pen register at *348issue in Smith. This mail cover did not include an examination of the contents of any mail. The postal officer merely recorded information appearing on the outside of mail addressed to the boxes which were the subject of the mail cover. The persons who sent or received mail knew or ought to have known that postal employees must examine the outside of the mail in order to deliver it. Furthermore, even if the plaintiffs did harbor a subjective expectation of privacy, that expectation was unreasonable. Persons who sent mail to the plaintiffs voluntarily exposed the information on the outside of the envelopes to postal employees. Courts that have addressed the question have uniformly upheld the constitutionality of mail covers on this reasoning. See United States v. DePoli, 628 F.2d 779 (2d Cir.1980); United States v. Huie, 593 F.2d 14 (5th Cir. 1979); United States v. Choate, 576 F.2d 165 (9th Cir.), cert. denied, 439 U.S. 953, 99 S.Ct. 350, 58 L.Ed.2d 344 (1978). Hence, we conclude that the mail cover in the instant case did not abridge the plaintiffs’ Fourth Amendment rights.
Ill
Finally, we address the issue whether the district court erred when it denied the plaintiffs’ motion for leave to file a second amended complaint. On appeal we must apply an abuse of discretion standard of review to this issue. R.E.B., Inc. v. Ralston Purina Co., 525 F.2d 749, 751 (10th Cir.1975). We have examined the written motion, its supporting argument and the remarks made by the plaintiffs’ counsel at the hearing. The plaintiffs do not contradict any significant statement in the defendants’ recital of uncontested facts. They have taken the depositions of defendants Davis and Stocks, postal employee Gordon Woffinder, and another person, Neal Colledge. They present no new legal theories or convincing argument that further discovery could help their case. The district court did not abuse its discretion by denying leave to amend. See O’Bryan v. Chandler, 352 F.2d 987, 990 (10th Cir.1965), cert. denied, 384 U.S. 926, 86 S.Ct. 1444, 16 L.Ed.2d 530 (1966).
AFFIRMED.
. Postal regulations contain the following definition of a mail cover:
“ ‘Mail cover’ is the process by which a record is made of any data appearing on the outside cover of any class of mail matter, including checking the contents of any second-, third-, or fourth-class mail as now
sanctioned by law, in order to obtain information in the interest of (i) protecting the national security, (ii) locating a fugitive, or (iii) obtaining evidence of commission or attempted commission of a crime.”
39 C.F.R. § 233.2(c)(1).
. Postal regulations define crime as “any commission of an act or the attempted commission of an act that is punishable by law by imprisonment for a term exceeding 1 year.” 39 C.F.R. § 233.2(c)(3).