In a synchronous remote mirroring system, as a host computer writes data to primary storage in a primary data storage system, remote copy data is transferred from the primary data storage system to a secondary storage system in which secondary storage is maintained as a remote mirror of the primary storage. The primary data storage system performs data reduction upon the remote copy data prior to transmitting the remote copy data in a reduced to the secondary data storage system. The secondary data storage system returns an acknowledgement of receipt of the remote copy data upon receipt of the remote copy data in the reduced form, and later reverses the data reduction upon the remote copy data in the reduced form to produce data written to the secondary storage to maintain the secondary storage as the remote mirror of the primary storage.