We suggest an analytic model of charge transport in weakly and heavily doped disordered organic materials. Doping of such materials increases the density of carriers but also creates deep Coulomb traps. The net effect is typically a decreasing mobility at low doping levels. At high doping levels the Coulomb traps overlap spatially, which leads to smoothening of the potential landscape and to strongly increasing mobility. The model is used to fit experimental data on the mobility in electrochemically (EC) doped polythiophenes. It also explains why increasing the carrier density by the field-effect results in a much higher mobility than an equivalent increase of the carrier density by EC doping.