Prime implicates have become a widely used tool in AI. The prime implicates of a set of clauses can be computed by repeatedly resolving pairs of clauses, adding the resulting resolvents to the set and removing subsumed clauses. Unfortunately, this brute-force approach performs far more resolution steps than necessary. Tison provided a method to avoid many of the resolution steps and Kean and Tsiknis developed an optimized incremental version. Unfortunately, both these algorithms focus only on reducing the number of resolution steps required to compute the prime implicates. The actual running time of the algorithms depends critically on the number and expense of the subsumption checks they require. This paper describes a method based on a simplification of Kean and Tsiknis’ algorithm using an entirely different data structure to represent the data base of clauses. The new algorithm uses a form of discrimination net called tries to represent the clausal data base which produces an improvement in running time on all known examples with a dramatic improvement in running time on larger examples.