A major aim of association studies is the identification of polymorphisms (usually SNPs) associated with a trait. Tests of association may be based on individual SNPs or on sets of neighboring SNPs, by use of (for example) a product P value method or Hotelling's T test. Linkage disequilibrium, the nonindependence of SNPs in physical proximity, causes problems for all these tests. First, multiple-testing correction for individual-SNP tests or for multilocus tests either leads to conservative P values (if Bonferroni correction is used) or is computationally expensive (if permutation is used). Second, calculation of product P values usually requires permutation. Here, we present the direct simulation approach (DSA), a method that accurately approximates P values obtained by permutation but is much faster. It may be used whenever tests are based on score statistics--for example, with Armitage's trend test or its multivariate analogue. The DSA can be used with binary, continuous, or count traits and allows adjustment for covariates. We demonstrate the accuracy of the DSA on real and simulated data and illustrate how it might be used in the analysis of a whole-genome association study.