The recent emergence of the high-efficiency video coding (HEVC) standard promises to deliver significant bitrate savings over current and prior video compression standards, while also supporting higher resolutions that can meet the clinical acquisition spatiotemporal settings. The effective application of HEVC to medical ultrasound necessitates a careful evaluation of strict clinical criteria that guarantee that clinical quality will not be sacrificed in the compression process. Furthermore, the potential use of despeckle filtering prior to compression provides for the possibility of significant additional bitrate savings that have not been previously considered. This paper provides a thorough comparison of the use of MPEG-2, H.263, MPEG-4, H.264/AVC, and HEVC for compressing atherosclerotic plaque ultrasound videos. For the comparisons, we use both subjective and objective criteria based on plaque structure and motion. For comparable clinical video quality, experimental evaluation on ten videos demonstrates that HEVC reduces bitrate requirements by as much as 33.2% compared to H.264/AVC and up to 71% compared to MPEG-2. The use of despeckle filtering prior to compression is also investigated as a method that can reduce bitrate requirements through the removal of higher frequency components without sacrificing clinical quality. Based on the use of three despeckle filtering methods with both H.264/AVC and HEVC, we find that prior filtering can yield additional significant bitrate savings. The best performing despeckle filter (DsFlsmv) achieves bitrate savings of 43.6% and 39.2% compared to standard nonfiltered HEVC and H.264/AVC encoding, respectively.