1. A method for managing a data storage system that includes primary and secondary storage subsystems, including respective first and second non-volatile storage media, the method comprising: maintaining a record on the secondary storage subsystem, which is predictive of locations to which data are to be written on the primary storage subsystem by a host processor; receiving at the primary storage subsystem, from the host processor, the data to be written to a specified location on the first non-volatile storage media; if the specified location is not included in the record, sending a message from the primary storage subsystem to the secondary storage subsystem so as to cause the secondary storage subsystem to update the record; signaling the host processor that the data have been stored in the data storage system responsively to receiving the data and, if the specified location was not included in the record, responsively to receiving an acknowledgment at the primary storage subsystem from the secondary storage subsystem indicating that the record has been updated; and storing the data in the specified location on both the first and second non-volatile storage media.