A hash function secure in the indifferentiability framework (TCC 2004) is able to resist allmeaningful generic attacks. Such hash functions also play a crucial role in establishing the security of protocols that use them as random functions. To eliminate multi-collision type attacks on the Merkle–Damgård mode (Crypto 1989), Lucks proposed widening the size of the internal state of hash functions (Asiacrypt 2005). The fast wide pipe (FWP) hash mode was introduced by Nandi and Paul at Indocrypt 2010, as a faster variant of Lucks' wide pipe mode. Despite the higher speed, the proven indifferentiability bound of the FWP mode has so far been only up to the birthday barrier of n/2 bits. The main result of this paper is the improvement of the FWP bound to 2n/3 bits (up to an additive constant). We also provide evidence that the bound may be extended beyond 2n/3 bits.