Positron emission tomography (PET) systems suitable for use with dirty (positron+prompt gamma) emitters are provided. One or more prompt gamma detectors are added to the PET system, where the prompt gamma detectors are responsive to the prompt gammas provided by the dirty emitter, but are not responsive to 511 keV annihilation photons. The prompt gamma detectors can surround the imaging PET detector array and/or be disposed as end caps relative to a generally cylindrical PET detector array. The prompt gamma detectors need not provide spatial resolution, because coincidence events in the PET detector array are classified as 2-photon or 3-photon events depending on whether or not there is a time-coincident signal from the prompt gamma detectors. One application of this approach is dual isotope PET where distinct tracers labeled with clean and dirty positron emitters are simultaneously imaged.