Crystalline rock formations are prime candidates for siting of repositories for radioactive and toxic wastes. Even the possibility of tenuous proximity of these sites to the biosphere requires realistic means of predicting subtle features of contaminant migration, such as very low-level seepage. We generate percolation clusters to reproduce the often observed ramified embedded fracture structures in these formations. Diffusion paths through these clusters and the shortest spans of rock between them can so significantly decrease contaminant breakthrough times that previous estimates can be in error by up to an order of magnitude. Our analysis suggests that current methods for determining the suitability of geological formations as natural barriers to contamination are inadequate, and may result in dangerously misleading conclusions. ¿ American Geophysical Union 1996