In a computer system with a memory hierarchy, when a high-level cache supplies a data copy to a low-level cache, the shared copy can be either volatile or non-volatile. When the data copy is later replaced from the low-level cache, if the data copy is non-volatile, it needs to be written back to the high-level cache; otherwise it can be simply flushed from the low-level cache. The high-level cache can employ a volatile-prediction mechanism that adaptively determines whether a volatile copy or a non-volatile copy should be supplied when the high-level cache needs to send data to the low-level cache. An exemplary volatile-prediction mechanism suggests use of a non-volatile copy if the cache line has been accessed consecutively by the low-level cache. Further, the low-level cache can employ a volatile-promotion mechanism that adaptively changes a data copy from volatile to non-volatile according to some promotion policy, or changes a data copy from non-volatile to volatile according to some demotion policy.