We consider the acquisition process in short-range (1~10 km) free-space optical communication between moving parties when covertness is the overriding system performance requirement. In order to maximize covertness, it is critical to minimize the time required for the acquisition phase, during which the party initiating contact must conduct a broad-field scan, and risks revealing his position. Assuming an elliptical Gaussian beam profile, we show how to optimize the beam divergence angles, scan speed and design of the raster scan pattern so as to minimize acquisition time. In this optimization, several constraints are considered, including: SNR required for accurate bearing detection and reliable decoding, limited receiver bandwidth, limited scanner speed, and beam divergence as limited by the scanner mirror dimensions. Design examples are given to illustrate the design procedure and by these examples, we show that the optimum beam profile is often elliptical with high eccentricity, though the search field is circularly symmetric.