We report on Hall transport measurements of two p-type Cd-doped InP epilayers and two Mg-doped InP layers with low compensation levels. The acceptor concentrations and the compensation ratios were determined with an extended-state Hall transport model, which provided a good description of the mobilities and the free-hole concentrations. Binding energies of 51 and 38.7 meV were measured for the purest Cd- and Mg-doped samples, respectively. Nearest-neighbor hopping was present in all samples, consistent with a model by Shklovskii and Efros. Saturation of the corresponding conductivity was observed in the Mg-doped samples, in excellent agreement with a model by Shklovskii and Yanchev. Variable-range hopping was observed below 6 K, and was found to be consistent with Mott's expression for the conductivity. An unusual sign reversal of the Hall constant was observed in the Mg-doped samples at the onset of impurity conduction.