Order, Supreme Court, New York County (Ronald A. Zweibel, J.), entered September 1, 2005, which granted petitioner tenant’s application to stay arbitration of an appraisal of the leased property demanded by respondent landlord, denied landlord’s “cross petition” seeking damages for breach of the parties’ lease and directed arbitration thereof, and denied landlord’s motion for pre-arbitration discovery, unanimously affirmed, with costs.
The arbitrability of the third appraiser’s valuation of the leased premises, which the lease provides is binding on the parties, is not an arbitrable issue. Previous judicial findings arguably to the contrary made in connection with prior lease renewals are not res judicata, since such findings were made before the parties executed the lease extension and modification agreement that changed the valuation procedure (see Kappas v T.W. Kutter, Inc., 192 AD2d 402, 402-403 [1993]). While both the pre and postmodification leases provided that the third appraiser’s valuation is binding, the former, but not the latter, also provided for “excluding [from the property’s value] such improvement costs and building costs as are paid for by the Tenant.” It was landlord’s position in the prior proceedings that since the appraisal procedure in the premodification lease made the amount of such exclusion entirely dependent on information supplied by *309tenant, “[t]he only option the landlord has to contest claimed tenant improvements is in the [arbitration] procedure.” In the postmodification lease, the exclusion for tenant improvement costs was dropped in favor of a calculation of rent based on a reduced fixed percentage of the appraised value (6% of value instead of 8% of value minus tenant improvements). Thus the appraisal provision in the modified lease leaves no conceivable basis for demanding arbitration (see Matter of American Silk Mills Corp. [Meinhard-Commercial Corp.], 35 AD2d 197, 200-201 [1970]). The application court also correctly determined that landlord’s breach of contract claim is arbitrable and that landlord’s mere interposition of such a claim, denominated a “cross petition,” in her opposition papers to tenant’s petition to stay arbitration did not constitute a waiver of her right to arbitrate (cf. Sherrill v Grayco Bldrs., 64 NY2d 261, 272, 273-274 [1985]). We also agree that landlord failed to make a sufficient showing of necessity to warrant court-ordered discovery (see International Components Corp. v Klaiber, 54 AD2d 550, 551 [1976]). Concur—Tom, J.E, Andrias, Saxe and Marlow, JJ.