A method is provided for a data storage system to move data from a source logical disk (LD) region to a target LD region while the data storage system remains online to a host. The method includes determining if a region move will create excessive load so the data storage system appears offline to the host. If not, the method includes causing writes to the source LD region to be mirrored to the target LD region, causing data in the source LD region to be copied to the target LD region, blocking reads and writes to the data storage system, and flushing dirty cache in the data storage system. If flushing the dirty cache is fast so the data storage system appears online to the host, the method includes updating mappings of the virtual volume to the LD regions and resuming the reads and writes to the data storage system.