When all explanatory variables are non-stochastic, the constraint on the dependent variables implies certain constraints on the error terms as well as the coefficients. If an explanatory variable appears in only one equation, it must have a coefficient of zero to satisfy Theorem. Therefore, it does not appear in any equation. This chapter describes the evaluation of constraint item (CI) estimation procedures, given that all explanatory variables are non-stochastic and that n is known. It utilizes the Theil's "Principles of Econometrics" as the source of the best linear unbiased (BLU) estimator of S and the conditions under which it is BLU. The coefficients of each explanatory variable appearing in the YM equation must equal minus the sum of the coefficients of that explanatory variable from the other M-1 equations.