White-box cryptosystems aim at providing security against an adversary that has access to the encryption process. As a countermeasure against code lifting (in which the adversary simply distributes the code of the cipher), recent white-box schemes aim for ‘incompressibility’, meaning that any useful representation of the secret key material is memory-consuming. In this paper we introduce a new family of white-box block ciphers relying on incompressible permutations and the classical Even-Mansour construction. Our ciphers allow achieving tradeoffs between encryption speed and white-box security that were not obtained by previous designs. In particular, we present a cipher with reasonably strong space hardness of 215 bytes, that runs at less than 100 cycles per byte.