Hash functions are an important cryptographic primitive. They are used to obtain a fixed-size fingerprint, or hash value, of an arbitrary long message. We focus particularly on the class of dedicated hash functions, whose general construction is presented; the peculiar arrangement of sequential and combinational units makes the application of pipelining techniques to these constructions not trivial. We formalize an optimization technique called quasi-pipelining, whose goal is to optimize the critical path and thus to increase the clock frequency in dedicated hardware implementations. The SHA-2 algorithm has been previously examined by Dadda et al, with specific versions of quasi-pipelining; a full generalization of the technique is presented, along with application to the SHA-1 algorithm. Quasi-pipelining could be as well applied to future hashing algorithms, provided they are designed along the same lines as those of the SHA family.