If track gets a hit in SCM cache and subsequently promoted to DRAM cache (at block 1202) then determination is made (at block 1204) as to whether new minimum retention times have been specified by the host application for the track for the DRAM cache. If so (“Yes” branch 1206), then the cache management application 116 updates (at block 1208) the minimum retention times for the track. If not (“No” branch 1210), then the cache management application 116 computes new remaining minimum time based on the calculation “SCM minimum time—Time stayed in SCM cache” (reference numeral 1212). This new minimum time is now stored as DRAM minimum retention time and SCM minimum retention time is set to 0. This is done because the track is getting good hits and should remain in faster cache (i.e., the DRAM cache) for the entirety of its remaining minimum retention time.