In a variance component model,(Formula presented.), Pukelsheim (1981) proved that the non-negative and unbiased estimation of the variance components σ(Formula presented.), j=1, …, c, entails a transformation of the original model to Q(Formula presented.) (called Q-reduced model). The maximum likelihood (ML) approach based on the likelihood of Q(Formula presented.) (denoted Q-ML) is considered and applied to an incomplete block design (IBD) model. The Q-ML estimators of variance components and are shown to be more efficient in the mean squared error sense than the non-negative MINQUE’s (minimum norm quadratic unbiased estimators) in the IBD. The effect of using Q-ML estimators of the variance components to estimate the variance ratio in the combined estimator of the treatment contrast is also considered.