Circuit reliability under random parametric variation is an area of growing concern. For highly replicated circuits, e.g., static random access memories (SRAMs), a rare statistical event for one circuit may induce a not-so-rare system failure. Existing techniques perform poorly when tasked to generate both efficient sampling and sound statistics for these rare events. Statistical blockade is a novel Monte Carlo technique that allows us to efficiently filter-to block-unwanted samples that are insufficiently rare in the tail distributions we seek. The method synthesizes ideas from data mining and extreme value theory and, for the challenging application of SRAM yield analysis, shows speedups of 10 - 100 times over standard Monte Carlo.