Host data stored in one or more source physical extents of non-volatile data storage is identified as valid and determined to be infrequently written by host I/O requests, and is therefore compressed to generate a highly compressed version of the valid host data. The highly compressed version is then stored into at least one target physical extent. The valid host data may be initially compressed before it is stored in the source physical extent(s), and may be re-compressed to generate the highly compressed version. If the valid host data is also infrequently read, it may be recompressed using larger blocks of host data than were used to perform the initial compression. The performance tier of the target physical extent may be different from (e.g. lower than) the performance tier of the source physical extent. The technology may be embodied in a background process such as a garbage collector.