A cryosurgical system and method for supplying cryogen to a probe (24). The system including a container filled with cryogen and having bellows (56) of a pump (18) submerged within said cryogen. Conduits fluidly interconnect the bellows (56) and a probe (24) that is outside the container to permit the cryogen to be forced from the bellows to the probe upon activation of pump (18). A pressure relief valve (22) is fluidly coupled to the conduits and positioned between the bellows (56) and the probe (24). 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 (22) is activated to lower the pressure of the cryogen to a running pressure.