Timing and energy resolutions of the bismuth germanate (Bi4Ge3O12) scintillation crystals were studied, with particular respect to a positron-camera application. In comparison with the NaI(Tl) system, the detection efficiency for annihilation radiation is more than triple, and coincidence detection efficiency is more than ten times as good. This paper explores the properties of the new scintillator material and their bearing on the spatial resolution and the efficiency of coincidence detection in positron cameras with stationary ring detectors.