Coulomb stress maps are produced by computing the tensorial stress perturbation due to an earthquake rupture and resolving this tensor onto planes of a particular orientation. It is often assumed that aftershock fault planes are ``optimally oriented''; in other words, the regional stress and coseismic stress change are used to compute the orientation of planes most likely to fail and the coseismic stress is resolved onto these orientations. This practice assumes that faults capable of sustaining aftershocks exist at all orientations, an assumption contradicted by the observation that aftershock focal mechanisms have strong preferred orientations consistent with mapped structural trends. Here we systematically investigate the best planes onto which stress should be resolved for the Landers, Hector Mine, Loma Prieta, and Northridge earthquakes by quantitatively comparing observed aftershock distributions with stress maps based on optimally oriented planes (two- and three-dimensional), main shock orientation, and regional structural trend. We find that the best model differs between different tectonic regions but that in all cases, models that incorporate the regional stress field tend to produce stress maps that best fit the observed aftershock distributions, although not all such models do so equally well. Our results suggest that when the regional stress field is poorly defined, or in structurally complex areas, the best model may be to fix the strike of the planes upon which the stress is to be resolved to that of the main shock but allow the dip and rake to vary.