SUMMARY ORDER

Plaintiff-appellant Brad Newby appeals from the May 11, 2005 judgment of the United States District Court for the Southern District of New York (Richard J. Holwell, Judge) rendering judgment for the defendants-appellees on Newby’s claims of breach of contract, fraud, and quantum meruit/unjust enrichment. On appeal, Newby argues that (1) because a contract may be formed by more than one writing, the district court erred in finding that no employment contract existed; (2) the district court erred when it denied Newby’s motion to reopen discovery following summary judgment for the defendants on two of Newby’s claims; and (3) the district court erred when it denied Newby’s motion to amend the pretrial order to add a new witness. We assume the parties’ familiarity with the facts and procedural history.

Newby’s first argument overlooks the fact that the district court held that no contract existed because a condition created by the parties was unsatisfied, not because the elements of an employment contract under New York law were unsatisfied. The district court applied the rule that “if the parties to an agreement do not intend it to be binding upon them until it is reduced to writing and signed *206by both of them, they are not bound and may not be held liable until it has been written out and signed.” Scheck v. Francis, 26 N.Y.2d 466, 469-70, 311 N.Y.S.2d 841, 260 N.E.2d 493 (1970). Circuit precedent requires us to find as a matter of law that the parties in this case intended to be bound only upon signature of the agreement by both parties. See Longo v. Shore & Reich, Ltd., 25 F.3d 94, 96-97 (2d Cir. 1994) (finding such an intent in reliance on a cover letter to a proposed agreement directing both parties to sign the agreement). Here, the proposed agreement directs Newby to sign and return it to the defendants — instructions consistent with the agreement’s blank lines for the signatures of Newby and defendant Purushothaman and its language anticipating acceptance by “signing and returning” the letter agreement.

This condition was unsatisfied. Newby admitted below that he never signed the revised offer sent by Purushothaman and does not press on appeal the argument, possibly hinted at below, that his signature on the original offer as changed by his handwritten edits satisfies the mutual-signature condition. Thus, we hold that the district court correctly granted summary judgment to the defendants on Newby’s breach-of-eontract claim.

We also reject Newby’s second and third arguments. Newby makes no serious argument that the district judge erred in refusing to reopen discovery on an element of a claim that had been in the complaint since the beginning of the case. See generally Fed.R.Civ.P. 26(b)(2) (providing that a district court may limit discovery if “the party seeking discovery has had ample opportunity by discovery in the action to obtain the information sought”). And Newby’s later motion to amend the pretrial order appears to be an attempt to circumvent this ruling by adding a witness that he could have identified before discovery closed and before the pretrial order was entered. It would have burdened the defendants to counter new expert testimony a few weeks before trial, and a district court may properly guard against the deadline slippage that might be expected from a last-minute pretrial-order amendment. We find no abuse of discretion in the district court’s decision. See Potthast v. Metro-North R.R. Co., 400 F.3d 143, 154 (2d Cir. 2005) (citing 6A Charles Alan Wright et al., Federal Practice and Procedure § 1527, at 287-89 (2d ed. 1990) (“If the evidence ... was within the knowledge of the party seeking modification [of a pretrial order] at the time of the conference ..., then [modification] may not be allowed.”)).

For the foregoing reasons, the district court’s judgment is AFFIRMED.