The apparent strong correlation between Coulomb stress changes and the spatial distribution of aftershocks suggests the possibility of making near-real-time estimations of areas at risk of experiencing off-fault aftershocks. In order to do this in practice a number of issues must first be addressed, including the extent to which the main shock slip must be known in detail before a meaningful stress map can be constructed. Here we investigate this issue by constructing a time-ordered sequence of slip solutions for the Landers earthquake, computing Coulomb stress changes for each solution, and quantitatively comparing the stress field with the observed aftershocks by (1) resolving the Coulomb stress change onto the aftershock nodal planes and calculating the percentage of events consistent with triggering and (2) constructing a two-dimensional map of Coulomb stress and computing the correlation coefficient between the positive and negative areas and the locations of the aftershocks. We find that slip solutions based on empirical relations and either focal mechanism or moment tensor data produce stress fields inconsistent with the observed spatial distribution of aftershocks, whereas slip solutions incorporating the correct rupture geometry but greatly simplified slip produce stress fields consistent with the aftershock distribution when very near-fault events are excluded. We further find that resolving stress perturbations onto earthquake nodal planes and computing the percentage of events experiencing positive Coulomb stress provides a poor measure of success because of the limited range of structures on which events occur and the compatibility of the main shock stress field with these structures. Our results support the hypothesis that Coulomb stress changes affect the spatial distribution of aftershocks and suggest that meaningful calculations of Coulomb stress can be made as soon as an earthquake's rupture geometry is well constrained.