In this paper we compare the power of the multivariate Haseman–Elston (MHE) test proposed earlier by Amos et al. (1990) and a computationally rapid new version of the multivariate Haseman–Elston test (NMHE) (Elston et al. 2000). We show that the power of NMHE was, for different simulation setups, identical or higher than that of MHE. In the bivariate case, the power of the NMHE method was somewhat less than that of the computationally intensive maximum likelihood variance components method (Amos et al. 2001). We present comparisons of the empirical distributions of the NMHE test to its limiting distributions for a range of numbers of traits. The distribution of the NMHE test appeared to conform satisfactorily to its limiting asymptotic distribution in large samples. Otherwise, empirical critical values for NMHE are somewhat higher than predicted, i.e. the test proposed by Elston et al. (2000) is non-conservative. The use of empirical critical values is therefore recommended for limited sample sizes (less than several hundred families). We also present the results of a linkage analysis performed by the NMHE method on a set of 4 body size-related traits. The method identified meaningful combinations of traits that showed significant linkage on chromosome 2 and suggestive linkage to regions on chromosomes 16 and 17.