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, the record including a designation of locations to which the host is expected to write in the near future; 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; making a determination that the specified location is not included in the record, and responsively to the determination 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, wherein sending the message causes the secondary storage subsystem to predict one or more further locations to which the host processor has not yet written the data and is expected to write the data in a subsequent write operation, and to set a number of predicted locations in the record corresponding to the one or more further locations; signaling the host processor that the data have been stored in the data storage system responsively to receiving the data and, upon having made the determination that 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.