Calculations of static stress changes due to large earthquakes have shown that the spatial distribution of aftershocks is predictable to first order, with aftershocks primarily occurring in areas experiencing positive stress changes. Delineation of these areas relies on resolving the stress perturbation onto planes with known orientations; common practice is to use poorly constrained regional stress information to compute optimally oriented failure planes, assuming that they exist everywhere. Here we show that this assumption is not supported by observation but rather that aftershock failure planes are controlled by geological structure. We argue that useful aftershock hazard estimates are better made by replacing information on regional stress with statistical measures of structural orientations.