The authors obtain expressions for the restricted least squares estimator and its covariance matrix in the classical regression model when the matrix of regressors is not necessarily of full rank. The standard expressions for the restricted least squares estimator are not usable in the short rank case because they rely on the unrestricted estimator. But, in the presence of restrictions, the restricted least squares estimator may be computable even if the unrestricted estimator is not. The authors' derivation produces some additional, useful algebraic results for least squares computation.