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Several extensions of the logic programming language Prolog to non H clauses use case analysis to handle non-H clauses. In this paper, analytical and empirical evidences are presented to show that, by making a set of clauses less non-H using predicate renaming, the performance of these case-analysis based procedures can be improved significantly. In addition, the paper also investigated the problem of efficiently constructing a predicate renaming that reduces the degree of non-Hness of a clause set maximally. It is shown that this problem of finding a predicate renaming to achieve minimal non-Hness is NP-complete.