This paper discusses the potential for improved detectors in Positron Emission Tomography (PET) and explores the ultimate limits that might be achieved in the areas of spatial resolution, sensitivity, and maximum imaging rates. It is shown that if an ultra-fast, high· efficiency scintillator and a thin, low-noise, positionsensitive photodetector were available, a multi-layer time-of-flight tomograph would be possible with a 10 em axial field of view, a 3-dimensional spatial resolution of 2 mm fwhm,.and >700,000 prompt unscattered coincidences per sec for 1 JLCi per cm 3 in a 20 em diam cylinder of water.