A differential snapshot is established and maintained for a set of files stored on a volume. Copy-on-write operations are avoided for logically insignificant moves of blocks, such as the block rearrangements characteristic of defragmentation utilities. A file system passes a block copy command to lower-level drivers that are to inform the snapshotter that a block move operation is not logically meaningful. When the logically insignificant move is of a block whose data forms part of the data captured in the snapshot virtual volume, and when the move is to a block location that is functioning as logical free space, the snapshotter can simply modify its block bitmap and update translation table entries without needing to perform a copy-on-write.