Multivariate estimation fitting a common structure to estimates of genetic and environmental covariance matrices is examined in a simple simulation study. It is shown that such parsimonious estimation can considerably reduce sampling variation. However, if the assumption of similarity in structure does not hold at least approximately, bias in estimates of the genetic covariance matrix can be substantial. For small samples and more than a few traits, structured estimation is likely to reduce mean square error even if bias is quite large. Hence such models should be used cautiously.