Preliminary results on 16 cm(2), position-sensitive silicon drift detectors, fabricted for the first time on p-type silicon substrates, are presented. The detectors were designed, fabricated, and tested recently at LBL and show interesting properties which make them attractive for use in future physics experiments. A pulse count rate of approximately 8 x 10(6) s(-1) was demonstrated by the p-type silicon drift detectors. This count rate estimate was derived by measuring simultaneous tracks produced by a laser which was collimated using a photolithographic mask.