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We study computational approaches for detecting SNP-SNP interactions that are characterized by a set of "two-locus, two-allele, two-phenotype and complete-penetrance" disease models. We argue that existing methods, which use data to determine a best-fitting disease model for each pair of SNPs prior to screening, may be too greedy. We present a less greedy strategy which, for each given pair of SNPs, limits the number of candidate disease models to a set of prototypes determined a priori.