In recent years variance components models have been developed for localising genes that
contribute to human quantitative variation. In typical applications one assumes a multivariate
normal model for phenotypes and estimates model parameters by maximum likelihood. For
the joint analysis of several correlated phenotypes, however, finding the maximum likelihood
estimates for an appropriate multivariate normal model can be a difficult computational task due
to complex constraints among the model parameters. We propose an algorithm for computing
maximum likelihood estimates in a multi-phenotype variance components linkage model that readily
accommodates these parameter constraints. Data simulated for Genetic Analysis Workshop 10 are
used to demonstrate the potential increase in power to detect linkage that can be obtained if
correlated phenotypes are analysed jointly rather than individually.