A Monte Carlo procedure for the construction of complementary cumulative distribution functions (CCDFs) for comparison with the U.S. Environmental Protection Agency (EPA) release limits for radioactive waste disposal (40 CFR 191, Subpart B) is described and illustrated with results from a recent performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP). The Monte Carlo procedure produces CCDF estimates similar to those obtained with importance sampling in several recent PAs for the WIPP. The advantages of the Monte Carlo procedure over importance sampling include increased resolution in the calculation of probabilities for complex scenarios involving drilling intrusions and better use of the necessarily limited number of mechanistic calculations that underlie CCDF construction.