Hole trapping has been investigated in a series of donor doped polymers containing different concentrations of traps with different depths. The mobilities decrease with increasing trap concentration and trap depth while the general features of the field and temperature dependencies remain unchanged. The results are discussed within the framework of the recent simulations of Wolf et al. and Borsenberger et al. and an early model due to Hoesterey and Letson. The results are in agreement with the simulations of Wolf et al. and Borsenberger et al. and confirm the argument that for shallow trapping the basic phenomenology of transport, as revealed by the field and temperature dependencies of the mobility, remain unchanged. Quantitatively, the effects of traps can be accounted for by the replacement of the energy width of the hopping site manifold (sigma) by an effective width (sigma) eff. However, the use of the Hoesterey-Letson formalism leads to some discrepancies with respect to different trap depths.