LEVAL, Circuit Judge:

Defendants appeal from a default judgment of the United States District Court for the Southern District of New York (Schwartz, J.), sitting in diversity and applying New York law, in an action to recover amounts allegedly owed by defendants as a result of certain securities transactions. The district court denied defendants' motion to dismiss for lack of personal jurisdiction under Fed. R. Civ. P. 12(b)(2), finding that the facts alleged in the complaint, if true, were sufficient to confer personal jurisdiction over the Venezuelan defendants under New York's long-arm statute. Without making findings as to the truth or falsity of plaintiff's jurisdictional allegations, the district court went on to grant plaintiff's motion for a default judgment in the amount of $378,993 pursuant to Fed. R. Civ. P. 55(a). Because the court failed to determine whether the defendants had in fact done what was alleged in the complaint — thereby subjecting themselves to the jurisdiction of the New York courts — we vacate the judgment and remand.

BACKGROUND

Plaintiff Credit Lyonnais Securities USA, Inc., is a New York-based securities and investment banking firm. Defendant Cavelba S.A. is a Venezuelan securities firm based in Caracas, Venezuela. Defendant Rafael Alcantara, a resident of Caracas and a Venezuelan national, is Cavelba's Chief Executive Officer and principal stockholder.

On August 9, 1996, plaintiff filed the instant suit in the district court. The complaint alleged the following. Since 1991 the defendants had engaged in numerous securities and arbitrage transactions with plaintiff, and had maintained an account with plaintiff for that purpose. Between approximately December 14, 1993 and February 4, 1994, defendants contracted to sell plaintiff specified shares of stock at an aggregate price of $449,656.50. Plaintiff then contracted to sell these securities to third parties. Defendants failed to deliver the securities.

The market for the securities defendants had failed to deliver increased. To cover the short positions in defendants' account, plaintiff paid $714,072.29. It debited defendants' account in the amount of $264,415.79 — the difference between the buy-in price and the contract price. After defendants failed to comply with plaintiff's numerous demands for payment, plaintiff brought suit.

When defendants failed to file an answer, plaintiff moved for a default judgment pursuant to Fed. R. Civ. P. 55, and the court signed an order to show cause as to why default should not be entered. Defendants opposed the motion for a default judgment and cross-moved to dismiss for lack of personal jurisdiction under Fed. R. Civ. P. 12(b)(2). In their moving papers, defendants asserted that for the entire time period during which plaintiff claimed the transactions took place, beginning on November 5, 1993, Cavelba was enjoined by the Venezuelan courts from doing business, its offices were closed, its membership on the Caracas stock exchange suspended, and its assets frozen. Alcantara asserted that he was in jail from December 17, 1993 until May 2, 1994, when the charges against him were found to be without merit and his assets returned to him. An affidavit of defense counsel asserted that while defendants had sold securities to plaintiff in the preceding years, between November 5, 1993 and June 22, 1994, defendants "did not sell any securities to the plaintiffs or any other person or entity anywhere in the world."

By written opinion dated April 28, 1998, the court denied defendants' motion to dismiss and granted plaintiff's motion for a default judgment. The court awarded damages in the amount of $378,993 — the amount of plaintiff's claim plus interest and costs. This appeal followed.

DISCUSSION

Because the court failed to conduct the necessary factual inquiry as to whether it had personal jurisdiction over defendants, we vacate the judgment and remand for further proceedings.

Motions to dismiss under Rule 12(b)(2) may, in part, test plaintiff's theory of jurisdiction and, in part, test the facts supporting the jurisdictional theory. District courts are afforded "considerable procedural leeway" in deciding them. Marine Midland Bank, N.A. v. Miller, 664 F.2d 899, 904 (2d Cir. 1981). In ruling on the theory of jurisdictional allegations, the court may provisionally accept disputed factual allegations as true. In making such a ruling, the court need only determine whether the facts alleged by the plaintiff, if true, are sufficient to establish jurisdiction; no evidentiary hearing or factual determination is necessary for that purpose. See id.

We find no error in Judge Schwartz's conclusion that plaintiff's allegations, if true, satisfy the jurisdictional requirements of New York's long-arm statute, N.Y.C.P.L.R. § 302(a)(1). The statute permits a court to exercise jurisdiction over a non-domiciliary defendant if 1) the defendant "transact[s] business" in New York, and 2) the cause of action arises out of that business activity, such that an "articulable nexus" exists between them. See CutCo Indus., Inc. v. McNaughton, 806 F.2d 361, 365 (2d Cir. 1986) (citing McGowan v. Smith, 52 N.Y.2d 268, 272 (1981)). A defendant transacts business in New York when he "purposefully avails" himself of the privilege of conducting business there, thus invoking the benefits and protections of New York law. See McKee Elec. Co. v. Rauland-Borg. Corp., 20 N.Y.2d 377, 382 (1967). Plaintiff alleged that defendants held an "active account" with plaintiff's firm in New York beginning in 1991, and that they agreed to sell plaintiff various securities through that account in a series of transactions in 1993 and 1994 that are the basis of the suit. We agree with the district court that these facts, if true, would be sufficient to establish personal jurisdiction over defendants under § 302(a)(1). See Picard v. Elbaum, 707 F. Supp. 144, 147 (S.D.N.Y. 1989) (citing Ehrlich-Bober Co. v. Univ. of Houston, 49 N.Y.2d 574 (1980)); L.F. Rothschild v. Thompson, 433 N.Y.S.2d 6 (1st Dep't 1980).

Although the allegations of the complaint may be deemed true to test the jurisdictional theory of the complaint, defendants here challenged not only the theory but also the facts on which jurisdiction was predicated. While a court may initially deny such a motion to the extent it attacks the plaintiff's theory of jurisdiction without conducting inquiry into the disputed jurisdictional facts, eventually it must determine whether the defendant in fact subjected itself to the court's jurisdiction. The plaintiff still must prove the jurisdictional facts by a preponderance of the evidence, either at an evidentiary hearing or at trial. See CutCo, 806 F.2d at 366; Marine Midland, 664 F.2d at 904. Because the court never determined whether plaintiff could establish the facts upon which jurisdiction depended, judgment should not have been entered.

Defendants further contend that the district court lacked personal jurisdiction over them because the summons and complaint were not served in accordance with the requirements of Fed. R. Civ. P. 4, New York's Civil Practice Law and Rules, and the Venezuelan Civil Code. Defendants did not, however, provide the district court with the specific allegations they now raise as to why service was defective; in their pleadings below, defendants made only conclusory assertions that service did not comply with the applicable rules. The claim is therefore waived.

Defendants also contend that the district court abused its discretion in refusing to relieve them of their default. Because we are remanding for further proceedings on the issue of personal jurisdiction, we need not rule on this question. Defendants will have the opportunity to renew their application for relief from the default. We note, however, that where, as here, a defendant opposes a plaintiff's motion for a default judgment (or moves to set aside a default judgment under Fed. R. Civ. P. 55(c)), the district court should consider three factors: 1) whether, and to what extent, the default was willful; 2) whether defendants have a meritorious defense; and 3) whether vacating the judgment would cause prejudice to the plaintiff. See SEC v. McNulty, 137 F.3d 732, 738 (2d Cir. 1998); Commercial Bank of Kuwait v. Rafidain Bank, 15 F.3d 238, 243 (2d Cir. 1994).

Finally, defendants claim the district court erred in awarding damages in the amount demanded by plaintiff without conducting an inquest into the proper measure of damages. We agree that the court did not have sufficient evidence to make a damages award. Rule 55(b)(2) provides that when granting a default judgment, if "it is necessary to take account or to determine the amount of damages or to establish the truth of any averment by evidence . . . the court may conduct such hearings or order such references as it deems necessary and proper." At the time judgment was entered, the court had before it only the allegations in the complaint and the affidavit of plaintiff's counsel, who did not purport to have personal knowledge of the facts, asserting an amount of damages sustained by plaintiff as a result of defendant's failure to deliver the securities. This was insufficient evidence upon which to enter the amount of the judgment. Even when a default judgment is warranted based on a party's failure to defend, the allegations in the complaint with respect to the amount of the damages are not deemed true. See Au Bon Pain Corp. v. Artect, Inc., 653 F.2d 61, 65 (2d Cir. 1981); Geddes v. United Financial Corp., 559 F.2d 557, 560 (9th Cir. 1977). The district court must instead conduct an inquiry in order to ascertain the amount of damages with reasonable certainty. See Transatlantic Marine Claims Agency, Inc. v. Ace Shipping Corp., 109 F.3d 105, 111 (2d Cir. 1997).

If the district court finds on remand both that it has jurisdiction over the defendants and that judgement should be entered against them, it nevertheless must determine the appropriate amount of damages, which involves two tasks: determining the proper rule for calculating damages on such a claim, and assessing plaintiff's evidence supporting the damages to be determined under this rule. Depending on the state of the record on remand, the latter task may require a hearing. See id. Plaintiff contends that no further inquiry was required because the amount defendants owe is "readily ascertainable through simple arithmetic." We reject plaintiff's argument because it assumes both the appropriateness of its theory or rule for calculating damages and the correctness of the figures upon which the calculations were made.

CONCLUSION

The judgment is vacated. The case is remanded for further proceedings, as outlined above.