We propose a constrained permutation test that assesses the significance of an observed quantitative trait locus effect against a background of genetic and environmental variation. Permutations of phenotypes are not selected at random, but rather are chosen in a manner that attempts to maintain the additive genetic variability in phenotypes. Such a constraint maintains the nonindependence among observations under the null hypothesis of no linkage. The empirical distribution of the lod scores calculated using permuted phenotypes is compared to that obtained using phenotypes simulated from the assumed underlying multivariate normal model. We make comparisons of univariate analyses for both a quantitative phenotype that appears consistent with a multivariate normal model and a quantitative phenotype containing pronounced outliers. An example of a bivariate analysis is also presented.