This paper is concerned with (1) the problem of the construction of lower-order models and (2) the Telated problem of the order determination of a real system based upon an estimated model with an overestimated order. Methods of the construction of stable lower-order models and the system-order determination are proposed. The approach adopted is to obtain a minimal realization of the original system by taking the principal components of the predictors of the outputs as the state and then to construct reduced models based upon a measure of reducibility defined in connection with the minimal realization algorithm. The measure of reducibility is useful to get a priori information about how small the order of the reduced model can be without much deterioration. Simulation studies are also carried out to demonstrate the effectiveness of the measure of reducibility and the proposed methods.