Recently an unusual dependence of the charge carrier drift mobility in molecularly doped polymers on the concentration of traps has been reported. This dependence differs from the expected inverse proportionality that should be valid for trap-controlled transport. Using the results of computer simulation we argue that the reason for this dependence is different regimes of charge carrier transport for layers with different trap concentrations, i.e., dispersive transport for small trap concentrations and nondispersive transport for high trap concentrations. Our results also show that mobility, as estimated from the time of intersection of the asymptotes to the plateau and trailing edge of the photocurrent transient, is very sensitive to variations of its shape and, in some cases, effectively masks the real concentration and field dependence of the true mobility.