New techniques and apparatus are presented which overcome some of the limitations of previous capacitance transient techniques and extend the useful range of capacitance transient measurements to intermediate depth impurity and defect states in semiconductors. This development greatly enhances the usefulness of capacitance techniques as a tool to study nonradiative recombination. These techniques and apparatus are used here to measure the electron-capture cross sections and concentrations of isolated oxygen donors and ZnO complex luminescence centers in p-type Zn- and O-doped GaP. These results agree with the donor-acceptor pairing theory and with the conclusion of previous capacitance measurements that the ioslated O donor is of negligible importance as a recombination center in these samples. Data is also presented which shows the effect of the junction electric field in greatly enhancing the thermal emission rate of electrons trapped in ZnO centers.