Small mineral grains of high uranium content were located in polished sections of 8 potsherds from Cyprus, England, Greece and Mexico, by induced fission-track mapping. Chemical compositions of these grains, determined by x-ray microprobe attachment to a scanning electron microscope, indicate they are zircons or apatites, highuranium minerals. Such radioactive inclusions offer excellent dating possibilities. The internal alpha dose rate for such inclusions far exceeds the beta and gamma dose rates for the rest of the sherd and the burial soil. A modification of thermoluminescence dating, using only thermoluminescence induced by alpha particles in high-uranium inclusions, is suggested. -- AATA