In high-performance processors, providing a fast cache hit time is one of the most important design issues, if not the most important one, since the cache hit time is one of the key determinants of the processor cycle time. Direct-mapped virtual caches would be a nice match with such high-speed processors since they have the potential for a very fast hit time. Their fast hit time comes mainly from two sources: (1) they do not require a preceding TLB access on a cache hit since they are accessed by virtual addresses; (2) they do not suffer from delays clue to additional comparators and multiplexers that would otherwise be present in the set-associative caches. However, their hit time advantage does not come without drawbacks. Being virtual caches, they require an anti-aliasing scheme (either in hardware or software) to solve the well-known synonym problem and, being direct-mapped caches, they yield higher miss ratios than set-associative caches of comparable size. This paper proposes a novel cache organization called V-P cache that improves the miss ratios of direct-mapped virtual caches. The key to the proposed scheme is the use of the physical address to re-access the cache when the cache access based on the virtual address is a miss. Therefore, a given memory block can be placed in two different sets, one based on the virtual address and the other based on the physical address. By providing the benefit of two-way set-associative caches, the proposed scheme can eliminate many misses due to conflicts among frequently used blocks that happen to be mapped to the same set. Another important benefit of the proposed scheme is that it reduces the so-called anti-aliasing misses that result from the accesses to the blocks previously evicted from the cache for anti-aliasing purposes. A quantitative evaluation based on trace-driven simulations using ATUM traces reveals that conventional direct-mapped virtual caches utilize only 50% of total cache blocks due to replacements of cache blocks for anti-aliasing purposes. The proposed V-P cache, on the other hand, is shown to utilize more than 80% of the total cache blocks. The results also show that this improved cache storage utilization yields miss ratio improvements of up to 25%.