Digital screening and diagnosis from cytology slides can be aided by capturing multiple focal planes. However, using conventional methods, the large file sizes of high-resolution whole-slide images increase linearly with the number of focal planes acquired, leading to significant data storage and bandwidth requirements for the efficient storage and transfer of cytology virtual slides. We investigated whether a sequence of focal planes contained sufficient redundancy to efficiently compress virtual slides across focal planes by applying a commonly available video compression standard, high-efficiency video coding (HEVC). By developing an adaptive algorithm that applied compression to achieve a target image quality, we found that the compression ratio of HEVC exceeded that obtained using JPEG and JPEG2000 compression while maintaining a comparable level of image quality. These results suggest an alternative method for the efficient storage and transfer of whole-slide images that contain multiple focal planes, expanding the utility of this rapidly evolving imaging technology into cytology.