Convergence behaviour of restricted maximum likelihood algorithms in multivariate analyses imposing a factor-analytic structure on covariance matrices is examined. Results indicate that estimation for such models can entail a more difficult maximisation problem than 'unstructured' estimation. On the other hand, if only factors explaining negligible variation are omitted, convergence can be faster as parameters at the boundaries of the parameter space have been eliminated. The 'parameter expanded' expectation maximisation algorithm tends to require many more iterates than the 'average information' algorithm, but is useful, in particular when combined with the latter.