As energy consumption of cache memories increases, an energy-efficient cache management mechanism is required. While a dynamic cache resizing mechanism is one promising approach to the energy reduction of microprocessors, one problem is that its effect is limited by the existence of dead-on-fill blocks, which are not used until their evictions from the cache memory. To solve this problem, this paper proposes a cache management policy named FLEXII, which can reduce the number of dead-on-fill blocks and help dynamic cache resizing mechanisms further reduce the energy consumption of the cache memories.