A method of cooling a material including the steps of (i) providing a cryotherapy instrument, (ii) positioning a portion of the cryotherapy instrument adjacent the material to be cooled, and (iii) circulating a cryogenic fluid through the cryotherapy instrument under physical conditions near a critical point of a liquid-vapor system for the cryogenic fluid. The critical point defines a point in a phase diagram of the liquid-vapor system where molar volumes are substantially equivalent for liquid and gas, whereby vapor lock associated with cooling of the cryotherapy instrument is avoided.