Approaches to selection of motion vector (“MV”) precision during video encoding are presented. These approaches can facilitate compression that is effective in terms of rate-distortion performance and/or computational efficiency. For example, a video encoder determines an MV precision for a unit of video from among multiple MV precisions, which include one or more fractional-sample MV precisions and integer-sample MV precision. The video encoder can identify a set of MV values having a fractional-sample MV precision, then select the MV precision for the unit based at least in part on prevalence of MV values (within the set) having a fractional part of zero. Or, the video encoder can perform rate-distortion analysis, where the rate-distortion analysis is biased towards the integer-sample MV precision. Or, the video encoder can collect information about the video and select the MV precision for the unit based at least in part on the collected information.