Skewed-associative caches have been shown to statisticaly exhibit lower miss ratios than set-associative caches at equal associativity degrees. But for L1 caches, the performance of a four-way set-associative cache is known to be quite close to that of a 16-way set-associative cache. In this paper, we first show that BTBs and L2 caches featuring long line size may benefit a lot from a high associativity degree on set-associative caches and a LRU replacement policy. Skewed-associative caches with an hypothetic LRU replacement policy «provide» this high associativity but with a low number of cache banks. Unfortunately, LRU replacement policies can not be easily implemented in hardware on skewed-associative caches. We propose some new replacement heuristics for skewed-associative caches. Those heuristics exhibit slightly worse behavior than a full LRU replacement policy, but still allow a 2-way skewed-associative cache to outperform a 4-way LRU set-associative cache and a 4-way skewed-associative cache to outperform a 16-way LRU set-associative cache. Therefore skewed-associativity allows significant miss reduction on BTBs and L2 caches.