Optimal GMM is known to dominate Gaussian QMLE in terms of asymptotic efficiency [Chamberlain, G., 1984. Panel data. In: Griliches, Z., Intriligator, M.D. (Eds.), Handbook of Econometrics, vol. II, pp. 1248-1313]. I derive a new condition under which QMLE is as efficient as GMM for a general class of covariance structure models. The condition trivially holds for normal data but also identifies non-normal cases for which Gaussian QMLE is efficient.