In this paper we introduce a model for studying meet-in-the-middle attacks on block ci-phers, and a simple block cipher construction provably resistant to such attacks in this model. A side-result of this is a proper formalization for an unproven alternative to DESX proposed by Kilian and Rogaway; this construction can now be shown to be sound in our model. Meet-in-the-middle attacks exploit weaknesses in key schedule algorithms, and building constructions resistant to such attacks is an important issue for improving the security of block ciphers. Our construction is generic so that it can be used on top of any block cipher, and it does not require to increase the key-length. We use an exposure resilient function (or ERF) as a building block and we propose a concrete and efficient instantiation strategy based on compression functions.