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.