In positron tomographs using a small number of position-sensitive detectors, each detector must operate at high singles event rates, especially during dynamic studies. To enable the PENN-PET tomography to perform studies involving high data rates, the high count rate behaviour of the position-sensitive scintillation detector used in the tomograph was investigated at singles rates in excess of 2 million counts per second (MCPS). Detector dead-time, minimised through the use of pulse clipping (clipping time, 120 ns), is a maximum of 20% at the highest data rates. At 2 MCPS and 240 ns pulse integration time, the full width at half maximum of the point spread function (PSF) worsens by approximately 20% over its low count rate value of 5.2 mm. Furthermore, at high count rates, pulse pile-up produces long tails in the PSF along the detector's long axis. These tails were reduced or eliminated through the use of a shortened pulse integration time (160 ns instead of 240 ns), an upper level energy discriminator and a local centroid event positioning algorithm. Detector performance was characterised for different combinations of these event processing techniques, and the mechanisms by which pulse pile-up distorts the high count rate PSF were investigated using computer simulations. With the incorporation of the high count rate event processing techniques, the detector's count rate capability enables the PENN-PET tomograph to handle most current imaging protocols.