Maximum likelihood procedures for estimating sum-constrained models like demand systems, brand choice models and so on, break down or produce very unstable estimates when the number of categories n is large as compared with the number of observations available T. In empirical studies this difficulty is mostly resolved by postulating the contemporaneous covariance matrix of the dependent variables to be equal to a2(I - n-il 1 1). In this paper we develop n n a maximum likelihood procedure based on a contemporaneous covariance matrix which allows that the variances per category may be different, while the number of observations required is substantially less than the number that would be required in the case of a completely unrestricted contemporaneous covariance matrix.