Distance bounding protocols aim at avoiding relay attacks during an authentication process. They are particularly awaited in RFID, where mounting a relay attack between a lowcapability prover and a remote verifier is no longer fiction. Several distance bounding protocols suited to RFID have been recently suggested, all targeting to reduce the two related quantities: adversary’s success probability and number of rounds executed within the protocol. Peinado, Ortiz, and Munilla introduced in 2006 an efficient distance bounding protocol that uses the concept of void challenges. We present in this paper a generic technique called MUltiState Enhancement that is based on a more efficient use of void challenges. MUSE significantly improves the performances of the already-published distance bounding protocols and extends the void challenges to p-symbols. Key words: RFID, Authentication, Mafia fraud, Distance bounding