Monte Carlo calculations of the efficiency of a small bismuth germanate detector are compared with experimental results. The calculations were made with a newly developed computer code PEP-C (for Photon-Electron-Positron transport in Cylindrical geometry) designed specifically for the computation of energy deposition spectra. Compared with existing transport codes, PEP-C incorporates several refinements in both the accuracy and efficiency of the particle tracking. Experimental data have been obtained for incident photons with energies in the range 0.059-8.062 MeV using calibrated radioactive sources, neutron activated sources and a radiative proton capture source. The calcllated data have a statistical uncertainty of no more than Â±2%, and agree with the measurements within the experimental uncertainty which varies from Â±2% at the low energies to Â±8% at the highest energy.