We exhibit a rich class of Horn clauses, which we call H1 , whose least models, though possibly infinite, can be computed effectively. We show that the least model of an H1 clause consists of so-called strongly recognizable relations and present an exponential normalization procedure to compute it. In order to obtain a practical tool for program analysis, we identify a restriction of H1 clauses, which we call H2 , where the least models can be computed in polynomial time. This fragment still allows to express, e.g., Cartesian product and transitive closure of relations. Inside H2 , we exhibit a fragment H3 where normalization is even cubic. We demonstrate the usefulness of our approach by deriving a cubic control-flow analysis for the Spi calculus  as presented in .