The coarse acquisition performance of a code-division multiple-access (CDMA) overlay system operating in a mobile communications environment is considered. Specifically, a CDMA system supporting communication between several mobile units and one base station shares the frequency band with an existing narrowband user. At the CDMA base station receivers, narrowband interference rejection filters are used to suppress the narrowband user's energy. It is demonstrated that in a nonfading environment the presence of the narrowband user does not severely affect the acquisition performance when the ratio of its bandwidth to the CDMA bandwidth is small. As the ratio becomes larger, the acquisition performance degrades, but the use of the interference rejection filter still significantly decreases the time to acquire. When flat Rician fading is introduced, the acquisition performance of the overlay system degrades, especially when the power in the direct component is small.