*579 WOOD, Circuit Judge.

This complex appeal arises from an order issued by the district court striking a motion to compel arbitration. The district court had pending before it questions relating to personal jurisdiction and venue. It decided to strike without prejudice the motion to compel arbitration pending resolution of those questions, but it indicated at the same time that it would welcome a refiling after the questions were sorted out. We find that this constitutes a “delay incident to an orderly process,” Middleby Corp. v. Hussmann Corp., 962 F.2d 614, 616 (7th Cir.1992), and that we therefore do not have appellate jurisdiction to hear an interlocutory appeal.

Continental Casualty, American Casualty, Transportation Insurance, and National Fire are all in the insurance business, affiliated as CNA. (When referring to them collectively, we will call them “CNA”; otherwise we will use the name of the particular corporation.) Continental also has two subsidiaries that figure prominently in this litigation: CNA ClaimPlus and RSKCo Services, Inc. RSKCo was the initial claims servicer for the agreements at stake here; ClaimPlus is, arguably, the successor claims servicer. Staffing Concepts and its similarly named affiliates are “professional employer organizations,” which take clients, employ their client’s employees, and lease the employees back to the clients. In effect, Staffing Concepts and its affiliates take care of the human resources paperwork for the client. We will refer to them collectively as “Staffing Concepts.” Staffing Concepts purchased workers’ compensation insurance policies from CNA.

This litigation revolves around two sets of agreements. The “Financing Agreements” deal with the financial side of the arrangements between CNA and Staffing Concepts, including the deductibles of the insurance plans. For the years relevant to this litigation (2001-03), Financing Agreements were struck between a subset of the CNA affiliates that changed each year and Staffing Concepts International (only). There is no arbitration clause in any of the Financing Agreements.

The “Claim Services Agreements” are the second set of agreements between the two sides; they focus on how claims are to be dealt with by each party. Unlike the Financing Agreements, the Claim Services Agreements have a consistent pair of signatories: RSKCo (a nonparty subsidiary of CNA) and Staffing Concepts International. The 2001 and 2002 Claim Services Agreements do contain broadly written arbitration clauses.

The litigation was set in motion when various Staffing Concepts entities made claims against the insurance policies. Under the policies, Staffing Concepts was allegedly supposed to reimburse CNA for the deductible portion of the claims it presented. CNA paid the claims Staffing Concepts presented, but Staffing Concepts did not reimburse CNA for the deductibles (which ran, CNA says, from $250,000 to $750,000 per claim). As a result, CNA asserts, it has incurred more than $44 million in losses. At some point, CNA replaced RSKCo with CNA ClaimPlus as the claims servicer.

On October 10, 2006, the four CNA insurers filed a complaint against the ten Staffing Concepts insureds for breach of the policies and Finance Agreements. At the same time, ClaimPlus (the claims ser-vicer) filed an arbitration claim against Staffing Concepts International, alleging a failure to pay claim handling fees. In theory, this had the effect of bifurcating the overall dispute into arbitrable claims that were sent to arbitration and nonarbi-trable claims that went to the district court.

*580 On December 7, 2006, Staffing Concepts National filed a motion to transfer venue to the United States District Court for the Middle District of Florida, while all of the other Staffing Concepts affiliates filed a motion to dismiss for lack of personal jurisdiction. Then on April 30, 2007, four of the Staffing Concepts family (Staffing Concepts International, Staffing Concepts, Inc., Staffing Concepts National, and Venture Resources Group) filed an answer to the complaint, containing both defenses and counterclaims against a shifting subset of the CNA insurers, as well as nonparty RSKCo.

On May 21, 2007, the CNA insurers moved to stay the district court proceedings in favor of the arbitration already underway between ClaimPlus and Staffing Concepts International. See 9 U.S.C. §§ 3-4. Two days later, the district court issued the order that gave rise to this appeal, stating that the motion “to dismiss or to stay Defendants’ Affirmative Defenses and Counterclaims in Favor of Prior Pending Arbitration ... is stricken without prejudice and may be refiled after [the] court rules on pending motions to dismiss for lack of personal jurisdiction and to transfer venue.”

This court immediately expressed its concerns about appellate jurisdiction and requested briefing on the subject, eventually postponing the issue for oral argument. Having heard both sides out on the matter, we ruled in an order issued January 11, 2008, that there is no proper appellate jurisdiction.

Under the Federal Arbitration Act, an appeal may be taken from a district court order “refusing a stay of any action ... under this title,” or “denying a petition ... to order arbitration to proceed.” 9 U.S.C. § 16. The district court here did neither: it struck the motion without prejudice, and at the same time it expressly invited a later refiling of the same motion. CNA equates every postponement with denial, while Staffing Concepts argues that a more finely tuned analysis is required. This particular order, it says, should be characterized as a “delay incident to an orderly process,” Middleby, 962 F.2d at 616, that does not constitute an appealable denial or refusal of the petition.

Middleby suggests that the relevant question here is similar to the question that arises when a court is considering an injunction: under what circumstances is a delay of a ruling equivalent to a denial. “The Supreme Court’s answer has been: when the passage of time causes irreparable injury to the person claiming entitlement to relief.” Id. Only if the CNA insurers can show irreparable harm resulting from the district court’s decision to take up personal jurisdiction and venue first can it demonstrate that the district court effectively denied its petition to compel arbitration, and thus that appellate jurisdiction exists under 9 U.S.C. § 16.

This court extended Middleby to the very situation presented to us here in IDS Life Ins. Co. v. SunAmerica, Inc., 103 F.3d 524, 526-27 (7th Cir.1996). In IDS, the district court left ambiguous whether it had granted or denied the stay on proceedings while it considered a preliminary injunction, but it invited a refiling after the preliminary injunction was straightened out. Applying Middleby, the court in IDS concluded that the district court’s deferral of consideration of the stay until after the preliminary injunction hearing did not give rise to an appealable order, explaining when justifiable delay is transformed into constructive denial of relief as follows:

A showing of unjustifiable delay coupled with irreparable injury if an immediate appeal is not allowed is enough to make a constructive denial appealable, if a formal denial would be_Maybe a show *581 ing of delay at once inordinate and unjustified, ... — the kind of thing that would excuse a person challenging administrative action from having to exhaust his administrative remedies, ... or an applicant for federal habeas corpus from having to exhaust his state remedies, ... — is also enough. Otherwise the lower court or agency would have the judicial or administrative equivalent of a pocket veto.

Id. at 526-27 (citations omitted).

Sharif v. Wellness Int'l Network, Ltd., 376 F.3d 720(7th Cir.2004), illustrates the other side of this coin. In that case, the district court never set a schedule for dealing with the motion to stay court proceedings in favor of arbitration and never even indicated when such a motion might be appropriate. Instead, the district court denied the motion, labeling it “superfluous” because of a pending venue motion. Id. at 726. Here, in contrast, the district court explicitly set its own affairs in order, indicating that it wanted to deal first with the venue and personal jurisdiction issues before turning to the motion to compel arbitration. In striking the motion with an invitation to refile, it signaled that it was not going to let the matter languish.

The only harms to which CNA points are those related to a then-approaching discovery deadline. This type of harm is easily averted, however, by a simple request to the district court for an order extending the deadline or limiting discovery to threshold issues of arbitrability. CNA did not do this; it chose to assume that all interim motions would be futile. More than that is necessary before we would jump to the conclusion that the district court was going to allow “inordinate and unjustified” time to pass before it ruled on the motion to compel arbitration.

The “delay incident to an orderly process” that occurred in this case provides no ground for appellate jurisdiction unless irreparable damage could be shown. CNA has shown none, and so there is no basis for us to hear its appeal. This appeal is DISMISSED for want of appellate jurisdiction.