A cryosurgical system and method for supplying cryogen to a probe. The system including a container filled with cryogen and having bellows of a pump submerged within said cryogen. Conduits fluidly interconnect the bellows and a probe that is outside the container to permit the cryogen to be forced from the bellows to the probe upon activation of pump. A pressure relief valve is fluidly coupled to the conduits and positioned between the bellows and the probe. After initially forcing cryogen to the probe at a pressure that establishes a colligative-based sub-cooling of the liquid cryogen, the pressure relief valve is activated to lower the pressure of the cryogen to a running pressure.