In this paper, we introduce a new class of double-block-length hash functions. Using the ideal cipher model, we prove that these hash functions, dubbed MJH, are asymptotically collision resistant up to O(2n(1−ϵ)) query complexity for any ϵ>0 in the iteration, where n is the block size of the underlying blockcipher. When based on n-bit key blockciphers, our construction, being of rate 1/2, provides better provable security than MDC-2, the only known construction of a rate-1/2 double-length hash function based on an n-bit key blockcipher with non-trivial provable security. Moreover, since key scheduling is performed only once per message block for MJH, our proposal significantly outperforms MDC-2 in efficiency. When based on a 2n-bit key blockcipher, we can use the extra n bits of key to increase the amount of payload accordingly. Thus we get a rate-1 hash function that is much faster than existing proposals, such as Tandem-DM with comparable provable security. This is the full version of Lee and Stam (A faster alternative to MDC-2, 2011).