We consider a video transmission system that supports digital pan/tilt/zoom by cropping the region-of-interest (RoI) chosen by the user and encoding it before transmission. With a static camera, the motion in the transmitted video results mostly from changing the RoI. We propose an efficient technique for cropping the RoI in a way that yields low-energy residual after motion compensation performed by a video encoder such as H.264/AVC. Experimental results indicate that the proposed technique can achieve a significant rate reduction of about 70% compared to compression-oblivious digital pan/tilt/zoom with negligible increase in system complexity.