Previous research has indicated that for dip-slip faults embedded in a half-space, the nonvertical, asymmetric fault geometry can have a significant effect on the seismic nucleation process. Using quasi-static simulation methods and a slip-weakening friction law, we investigate the coupled effects of asymmetric fault geometry and depth-dependent frictional properties on seismic nucleation on dip-slip faults. As a first-order approximation to the depth-dependent parameters in the Earth, we assume that the normal stress tapers to a small value near the free surface, and we assume that the drop in frictional coefficient decreases with depth. We find that these depth-dependent properties have an important effect on the nucleation process of these faults: Compared to models with homogeneous frictional properties, the nucleation point moves down dip, the time to unstable slip nucleation decreases, and the amount of preseismic surface slip increases significantly. However, these effects do not dominate the effects of the asymmetric dipping geometry of these faults on the nucleation process: thrust faults nucleate farther up dip than normal faults and nucleate earlier as well. Normal faults have a larger amount of preseismic surface slip than thrust faults. The results indicate that both geometrical and frictional heterogeneity can have important effects on nucleation and that both sources of complexity must be taken into account to produce accurate models of the seismic nucleation process.