The analysis of gamma-ray spectra measured with a scintillation counter with an anticoincidence annulus is described in detail. In particular the problem of the determination of the energy and intensity of gamma rays from such measurements is considered. The shapes of the full-energy peaks in observed complex spectra are studied and an attempt is made to justify their description in terms of a Gaussian response function. The details of the statistical analysis of complex gamma-ray spectra are given and, finally, procedures which have been used to confirm the validity of error estimates in energy and intensity measurements are described.