This paper investigates the power saving mechanism of Universal Mobile Telecommunications System (UMTS). UMTS discontinuous reception (DRX) is exercised between the network and a mobile station (MS) to save the power of the MS. The DRX mechanism is controlled by two parameters: the inactivity timer threshold tI and the DRX cycle tD. Analytic analysis and simulation model are proposed to study the optimal tI and tD selections that maximize the MS power saving under the given mean packet waiting time constraint. We also devise an adaptive algorithm called dynamic DRX (DDRX). This algorithm dynamically adjusts the tI and tD values to enhance the performance of UMTS DRX. Our study quantitatively shows how to select the best inactivity timer and DRX cycle values for various traffic patterns. We also show that DDRX nicely captures the user traffic patterns, and always adjusts the tI and tD close to the optimal values.