With z/OS V2R1, a ZCOMPRESS parameter has been added to the SETSYS command. It allows DFSMShsm to specifying the type of compression used during migration or backup for all data sets.
For more information, refer to the topic covering the SETSYS command in z/OS DFSMShsm Storage Administration.
For more information on zEDC, see Using the zEnterprise Data Compression (zEDC) enhancements.