
616 F.3d 612 (2010)
LEISURE CAVIAR, LLC; Bemka Corporation, Plaintiffs-Appellants,
v.
UNITED STATES FISH AND WILDLIFE SERVICE; Tim Van Norman, in his capacity as Chief of the Branch of Permits, Division of Management Authority, United States Fish and Wildlife Service; Jorge Villavicencio, in his capacity as an employee of the Branch of Permits, Division of Management Authority, United States Fish and Wildlife Service, Defendants-Appellees.
No. 09-6228.
United States Court of Appeals, Sixth Circuit.
August 19, 2010.
*614 ON BRIEF: James R. McKoon, McKoon, Williams & Haun, Chattanooga, Tennessee, for Appellants. M. Kent Anderson, Assistant United States Attorney, Chattanooga, Tennessee, for Appellees.
Before: SUTTON and McKEAGUE, Circuit Judges; JONKER, District Judge.[*]

OPINION
SUTTON, Circuit Judge.
Leisure Caviar, a wholesale dealer of paddlefish roe, and Bemka Corporation, a buyer of paddlefish roe, challenge the district court's denial of their Rule 59 motion to alter or amend the order dismissing their suit against the United States Fish and Wildlife Service and two of its employees. They also challenge the rejection of their post-dismissal Rule 15 motion to revise their amended complaint. Because the plaintiffs have not shown that any "newly discovered evidence" was "previously unavailable," GenCorp, Inc. v. Am. Int'l Underwriters, 178 F.3d 804, 834 (6th Cir.1999), we affirm.

I.
The Fish and Wildlife Service is responsible for regulating and managing the export and sale of paddlefish roe, see 50 C.F.R. §§ 23.1, 23.71, in accordance with the requirements of the Convention on International Trade in Endangered Species of Wild Fauna and Flora ("the Convention"), 27 U.S.T. 1087, and the Endangered Species Act of 1973, 16 U.S.C. §§ 1531-44. To qualify for a paddlefish roe export permit, an applicant must show that it properly harvested the roe and that its export would not undermine the survival of the species. See 50 C.F.R. §§ 23.36, 23.60, 23.61.
Leisure Caviar and Bemka sued the Fish and Wildlife Service and two of its employees in their official capacities, alleging that the agency failed to act on a timely basis on five permit applications, all pending for seven to twelve months, for permission to export 4074.05 pounds of roe worth approximately $500,000. Because paddlefish roe "has a shelf-life of approximately 12-15 months," they said, the agency's failure to grant or deny the export permits put their entire investment "in the harvesting, curing and marketing of the paddlefish roe ... at risk of being lost." R.1 ¶¶ 18, 21. The plaintiffs sought a court order compelling the agency immediately to process its applications. See 5 U.S.C. § 706 (a reviewing court may "compel agency action ... unreasonably delayed"); 28 U.S.C. § 1361 (writ of mandamus).
The agency moved to dismiss the action under Rules 12(b)(1) and 12(b)(6) of the Federal Rules of Civil Procedure. It argued that the plaintiffs had failed to exhaust their administrative remedies, a prerequisite for bringing suit against the government under the Federal Tort Claims Act (FTCA), 28 U.S.C. § 2675(a), and that the plaintiffs had failed to state a *615 cause of action for violation of any constitutional rights or otherwise to provide any cognizable basis for obtaining mandamus relief.
The court granted the motion to dismiss. It first ruled that the plaintiffs had failed to exhaust their administrative remedies and thus could not bring an FTCA claim. It then ruled that the processing of applications under the Convention amounts to a discretionary responsibility, one ineligible for mandamus relief. See Pittston Coal Group v. Sebben, 488 U.S. 105, 121, 109 S.Ct. 414, 102 L.Ed.2d 408 (1988).
The plaintiffs asked the court to alter or amend the judgment, see Fed.R.Civ.P. 59(e), then separately filed a motion for leave to amend their complaint, see Fed. R.Civ.P. 15(a). In denying the plaintiffs' motion to alter the judgment, the court reasoned that the plaintiffs had failed to demonstrate that their "newly discovered" evidence "was unavailable prior to [the] Court's ruling on Defendants' Motion to Dismiss." R.69 at 4. As for the plaintiffs' other arguments, the court ruled that they all had been raised in earlier motions and filings, and Rule 59(e) "does not afford parties an opportunity to reargue their case." Id. at 5. The court also denied the claimants' motion to amend the complaint.

II.
Plaintiffs contend that the court erred (1) in refusing to grant their motion to alter the judgment and (2) in refusing to allow them to amend their complaint.
The basics for obtaining relief under either theory are straightforward. Under Rule 59, a court may alter the judgment based on: "(1) a clear error of law; (2) newly discovered evidence; (3) an intervening change in controlling law; or (4) a need to prevent manifest injustice." Intera Corp. v. Henderson, 428 F.3d 605, 620 (6th Cir.2005). Under Rule 15, a court may grant permission to amend a complaint "when justice so requires" and in the normal course will "freely" do so. Fed.R.Civ.P. 15(a); see Foman v. Davis, 371 U.S. 178, 182, 83 S.Ct. 227, 9 L.Ed.2d 222 (1962); Benzon v. Morgan Stanley Distribs., Inc., 420 F.3d 598, 613 (6th Cir. 2005). A district court, generally speaking, has considerable discretion in deciding whether to grant either type of motion, and as a result we review these types of decisions for abuse of discretion. See Morse v. McWhorter, 290 F.3d 795, 799 (6th Cir.2002).
Plaintiffs' requests come with two twists. In the first place, what looks like multiple requests for relief amounts in reality to just oneor at least just one theory of relief. Their Rule 59 position is not that the district court erred in granting the motion to dismiss based on the existing pleadings. Plaintiffs, indeed, nowhere challenge the court's resolution of the motion to dismiss. They instead argue that the judgment should be altered to allow them to amend their complaint based on newly discovered evidence, which allegedly turned up for the first time during discovery. The essence of their appeal, then, turns on a rejected request to amend their complaint due to newly discovered evidence, which at this stage of the case requires a district court to grant relief under Rule 15 and Rule 59. See Foman, 371 U.S. at 182, 83 S.Ct. 227; Benzon, 420 F.3d at 613; Morse, 290 F.3d at 800.
In the second place, this is not a traditional motion to amend the complaint. Rule 15 requests to amend the complaint are frequently filed and, generally speaking, "freely" allowed. But when a Rule 15 motion comes after a judgment against the plaintiff, that is a different story. Courts in that setting must "consider[ ] the competing interest of protecting the finality of *616 judgments and the expeditious termination of litigation." Morse, 290 F.3d at 800. If a permissive amendment policy applied after adverse judgments, plaintiffs could use the court as a sounding board to discover holes in their arguments, then "reopen the case by amending their complaint to take account of the court's decision." James v. Watt, 716 F.2d 71, 78 (1st Cir.1983) (Breyer, J.). That would sidestep the narrow grounds for obtaining post-judgment relief under Rules 59 and 60, make the finality of judgments an interim concept and risk turning Rules 59 and 60 into nullities. See 6 Charles Alan Wright, Arthur R. Miller & Mary Kay Kane, Federal Practice and Procedure § 1489 (3d ed.2010).
When a party seeks to amend a complaint after an adverse judgment, it thus must shoulder a heavier burden. Instead of meeting only the modest requirements of Rule 15, the claimant must meet the requirements for reopening a case established by Rules 59 or 60. See In re Ferro Corp. Derivative Litig., 511 F.3d 611, 624 (6th Cir.2008); United States ex rel. SNAPP, Inc. v. Ford Motor Co., 532 F.3d 496, 507 (6th Cir.2008). In post-judgment motions to amend, as a result, "the Rule 15 and Rule 59 inquiries turn on the same factors." Morse, 290 F.3d at 799. A court acts within its discretion in denying a Rule 15 and a Rule 59 motion on account of "undue delay"including delay resulting from a failure to incorporate "previously []available" evidence, GenCorp, 178 F.3d at 834and ought to pay particular attention to "the movant's explanation for failing to seek leave to amend prior to the entry of judgment." Morse, 290 F.3d at 800.
Neither party disputes these rules or these considerations. They instead take sides on how to apply them. Plaintiffs say that the district court abused its discretion in denying their motions because the discovery process yielded important new information that casts a different light on the dispute, requiring the court to reconsider its decision. But there is less to the evidence obtained in discovery than plaintiffs suggest.
First, they claim that Jorge Villavicencio, a biologist with the Fish and Wildlife Service, admitted in his deposition testimony "to threatening Plaintiffs with future handling of applications outside of the bounds of applicable regulations" and to having done so at the instruction of Timothy Van Norman, his supervisor. R.51 at 4-5; see R.60-2 at 74-80. This admission, they argue, establishes the predicate for a new retaliation claim against Villavicencio and Van Norman in their individual capacities. The problem with this argument is that the alleged threat came in the form of an email, an email the plaintiffs mentioned in their first amended complaint. The plaintiffs were thus already on notice of Villavicencio's alleged misconduct and had no reasonother than news that the court had dismissed their first amended complaintto wait for this deposition testimony to press a claim for retaliation. A plaintiff cannot use a Rule 59 motion (or for that matter a post-judgment Rule 15 motion) "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).
Second, plaintiffs claim that they were "informed" during discovery that the government offered leniency to an unnamed defendant in an unrelated criminal case in exchange for information incriminating Leisure Caviar and its controlling member. This information, plaintiffs say, supports an additional cause of action against "Unknown Named Agent(s)" of the agency. R.60-4 ¶ 39. But plaintiffs offered *617 no deposition testimony, no affidavit, no identifying detailsno evidence at allto corroborate this new claim. A district court does not abuse its discretion by rejecting an unsupported theory for amending a complaint.
Third, plaintiffs asked to add a claim charging the agency with having insufficient resources to process paddlefish roe permit applications in a timely manner, depriving applicants of their property rights without due process of law. Some of the deposition testimony, it is true, bolsters this claim. See, e.g., R.60-3 at 168-69 ("[the agency] is underfunded and understaffed"). But so, too, do several passages from the plaintiffs' original complaint: "[P]ermit applications have been pending before [the agency] for at least seven (7) months, and as long as approximately one year," R.1 ¶ 17; "[p]addlefish roe is a perishable good, and ... [the agency] is aware of this time limitation," Id. at ¶ 18; "[the agency] ... owes a duty to Leisure Caviar and Bemka ... to process applications for [export] permits in a timely manner," Id. at ¶ 19; "the entire significant investment ... [in] paddlefish roe is at risk of being lost," Id. at ¶ 21. As their original complaint establishes, the plaintiffs knew that the agency was having trouble keeping up with the influx of applications when they first filed the lawsuit and that this delay threatened to destroy their investment. The district court did not abuse its discretion in ruling that the plaintiffs could have filed this claim before they lost the original case.
Fourth, plaintiffs contend that deposition testimony supported their proposed additional claim "challenging the constitutionality of the permitting process." R.60 at 2. The agency, they say, "has failed to create clear guidelines ... which limit official discretion in order to preclude arbitrary discrimination," R.60-4 ¶ 40, citing testimony that agents "have discretion within [the] office in making [legal acquisition] determinations," R.60-1 at 39-40, that no written protocols govern what documents the biologists place in the administrative record, and that the agency has no official handbook concerning paddlefish roe.
It may be true that this information was "newly discovered" in one sense, in that the plaintiffs apparently first learned about it during discovery. But the information should not have come as a surprise. From the beginning, the agency has maintained that the "issuance of export permits is not a ministerial duty but is a discretionary decision based on investigations and findings" by the agency. R.15 at 14. And the relevant regulationsall publicconfirm the nature and scope of this discretion. They require permit applicants to "provide sufficient information for [the agency] to find that your proposed activity meets all of the following criteria," including that "[t]he wildlife or plant was legally acquired" and that "[t]he proposed export would not be detrimental to the survival of the species." 50 C.F.R. § 23.36(c). In making such "finding[s]," officials "consider" a range of "factors" and a "continuum of risk." 50 C.F.R. § 23.60(d). These regulations put the plaintiffs on notice about the discretionary nature of the government employees' responsibilities. The district court, as a result, acted within its discretion in reasoning that the plaintiffs failed to explain why they could not previously have learned of the agency officials' discretionary role. "To constitute `newly discovered evidence,' the evidence must have been previously unavailable." GenCorp, 178 F.3d at 834. That was not so. A claimant who seeks to amend a complaint after losing the case must provide a compelling explanation to the district court for granting the motion. *618 The district court did not exceed its discretion in concluding that plaintiffs provided nothing of the sort.

III.
For these reasons, we affirm.
NOTES
[*]  The Honorable Robert J. Jonker, United States District Judge for the Western District of Michigan, sitting by designation.
