We introduce a new organization for multi-bank caches: the skewed-associative cache. A two-way skewed-associative cache has the same hardware complexity as a two-way set-associative cache, yet simulations show that it typically exhibits the same hit ratio as a four-way set associative cache with the same size. Then skewed-associative caches must be preferred to set-associative caches. Until the three last years external caches were used and their size could be relatively large. Previous studies have showed that, for cache sizes larger than 64 Kbytes, direct-mapped caches exhibit hit ratios nearly as good as set-associative caches at a lower hardware cost. Moreover, the cache hit time on a direct-mapped cache may be quite smaller than the cache hit time on a set-associative cache, because optimistic use of data flowing out from the cache is quite natural. But now, microprocessors are designed with small on-chip caches. Performance of low-end microprocessor systems highly depends on cache behavior. Simulations show that using some associativity in on-chip caches allows to boost the performance of these low-end systems. When considering optimistic use of data (or instruction) flowing out from the cache, the cache hit time of a two-way skewed-associative (or set-associative) cache is very close to the cache hit time of a direct-mapped cache. Therefore two-way skewed associative caches represent the best tradeoff for today microprocessors with on-chip caches whose sizes are in the range of 4-8K bytes.