Ongoing deformation of southern California is simulated in a set of 63 models in an attempt to empirically determine fault friction. To a previous code for simulation of anelastic crustal strain, we introduce a new finite element to represent a curved fault of arbitrary rheology. We also add several self consistent patterns of horizontal drag on the base of the crust caused by independent upper mantle flow. A grid of isoparametric finite elements represents the regional fault geometry and the known variations in elevation and heat flow. Plate tectonic velocity boundary conditions are applied. Solutions include the time-averaged flow velocities and fault slip rates and vertically averaged stresses. Each model is scored by comparing its slip rate predictions with 56 rates from dated offset geologic features. In membrane stress models the optimal fault friction is 0.4--0.6. Frictional self-heating of faults is not a major factor determining strength. Addition of crust-mantle coupling improves results if convergence of North American and Pacific lithospheres is assumed to occur under the Transverse Ranges. Among such models, those with fault friction of about 0.3 score best by most norms of the prediction error. These have over 80% of regional strain in faults and only a small amount of block deformation. However, one model with friction of 0.85 scores better by the percent of correct predictions norm. This model has only half the regional strain as a fault slip and matches slow rates well but underpredicts slip rates over 1 cm/yr. Furthermore, its predictions are degraded considerably if hydraulic lubrication of thrust faults is assumed; the low-friction models are unaffected. We conclude that some source of variation in fault friction remains unmodeled but that at least the fast-slipping faults in California have ''low'' friction, similar to that of hydrated clay gouges.