We evaluate the implications of several attenuation relationships, including three customized for southern California, in terms of accounting for site effects in probabilistic seismic hazard studies. The analysis is carried out at 43 sites along a profile spanning the Los Angeles basin with respect to peak acceleration, and 0.3-, 1.0-, and 3.0-sec response spectral acceleration values that have a 10% chance of being exceeded in 50 years. The variability among currently viable attenuation relationships (espistemic uncertainty) is an approximate factor of 2. Biases between several commonly used attenuation relationships and southern California strong-motion data imply hazard differences that exceed 10%. However, correcting each relationship for the southern California bias does not necessarily bring hazard estimates into better agreement. A detailed subclassification of site types (beyond rock versus soil) is found to be both justified by data and to make important distinctions in terms of hazard levels. A basin depth effect is also shown to be important, implying a difference of up to a factor of 2 in ground motion between the deepest and shallowest parts of the Los Angeles basin. In fact, for peak acceleration, the basin-depth effect is even more influential than the surface site condition. Questions remain, however, whether basin depth is a proxy for some other site attribute such as distance from the basin edge. The reduction in prediction error (sigma) produced by applying detailed site and/or basin-depth corrections does not have an important influence on the hazard. In fact, the sigma reduction is less than epistemic uncertainties on sigma itself. Due to data limitations, it is impossible to determine which attenuation relationship is best. However, our results do indicate which site conditions seem most influential. This information should prove useful to those developing or updating attenuation relationships and to those attempting to make more refined estimates of hazard in the near future.