This paper is based on findings resulting from ASHRAE Research Project RP-1472.Cryosurgery is a technique for destroying undesirable tissue such as cancers using a freezing process. A thermodynamic modeling tool was developed for a two stage, mixed gas Joule-Thomson (MGJT) cryoprobe used for cryosurgery. A conventional Vapor Compression (VC) cycle using a pure refrigerant pre-cools the MGJT cycle that provides refrigeration at the cryoprobe tip. The model is used with an optimization routine to investigate the optimal mixture composition for different cryoprobe tip temperatures as well as optimal precooling temperatures. The cryoprobe system performance is reported in terms of cryoprobe size, and compressor size and power consumption. The results for the two stage system are compared with the performance of a single stage MGJT cycle to demonstrate the benefits and limitations associated with the addition of the precooling cycle.Units: Dual