Genetic association studies achieve an unprecedented level of resolution in mapping disease genes by genotyping dense single nucleotype polymorphisms (SNPs) in a gene region. Meanwhile, these studies require new powerful statistical tools that can optimally handle a large amount of information provided by genotype data. A question that arises is how to model interactions between two genes. Simply modeling all possible interactions between the SNPs in two gene regions is not desirable because a greatly increased number of degrees of freedom can be involved in the test statistic. We introduce an approach to reduce the genotype dimension in modeling interactions. The genotype compression of this approach is built upon the information on both the trait and the cross-locus gametic disequilibrium between SNPs in two interacting genes, in such a way as to parsimoniously model the interactions without loss of useful information in the process of dimension reduction. As a result, it improves power to detect association in the presence of gene-gene interactions. This approach can be similarly applied for modeling gene-environment interactions. We compare this method with other approaches, the corresponding test without modeling any interaction, that based on a saturated interaction model, that based on principal component analysis, and that based on Tukey's one-degree-of-freedom model. Our simulations suggest that this new approach has superior power to that of the other methods. In an application to endometrial cancer case-control data from the Women's Health Initiative, this approach detected AKT1 and AKT2 as being significantly associated with endometrial cancer susceptibility by taking into account their interactions with body mass index.