Lapusta et al., 2000 have developed an efficient and rigorous numerical procedure for elastodynamic analysis of earthquake sequences on slowly loaded faults. This is done for a general class of rate and state friction laws with positive direct velocity effect. We use the procedure to study the response of a 2-D strike-slip fault model with depth-variable properties. We find the following (as partially reported by Lapusta et al., 2000: Small events appear in increasing numbers for decreasing values of the characteristic slip distance of the friction law. The nucleation phase of small and large events is very similar. For a large event that is preceded by a small event (and hence heterogeneous stress distribution), moment acceleration in the beginning of dynamic propagation exhibits "slow-downs" and subsequent "speed-ups", consistently with some observations. Insufficient time and space discretization qualitatively changes the results. Incorporating slow tectonic loading is essential for uncovering the true model response.