Determination of dopant concentrations and mobilities is highly relevant for compensated silicon materials but crucial as standard models and standard methods fail due to the presence of multiple dopant species. Thus, an alternative method for direct determination of the net doping concentration p0 is presented, which is based on measurements of the free carrier absorption (FCA) with the help of Fourier Transform Infrared Spectroscopy (FTIR) and enables the majority carrier conductivity mobilities to be determined purely experimentally. Using a set of p-type FZ-silicon samples with a wide range of base resistivities, accuracy of the FTIR-FCA method for determining p0 and of the iron-boron pairing association time method for determining the total boron concentration are evaluated in depth and found to be highly satisfactory. These methods are applied to a set of samples from three compensated silicon crystals, with large differences in the dopant concentrations and the compensation ratio. Measurements of the dopant concentrations and the majority carrier conductivity mobilities as a function of ingot position indicate that the Klaassen mobility model is a good description for the conductivity mobility in compensated p-type silicon for a wide range of dopant concentrations.