A control layer of a data storage system is configured to identify one or more physical data units in the physical storage, which are associated only with corresponding logical snapshot data units, and to reallocate such physical snapshot data units to a dedicated storage space. The dedicated storage space can be a low-power storage space, which includes one or more disks designated as low power disks. The reallocation of snapshot data units to low power disks can be carried out according to an energy-aware migration policy, directed for minimizing the activation of the low power disks, and maintaining the disks in an inactive state for longer periods of time.