The order of the stabilizing controller and the closed-loop eigenvalues in LTI control systems designed using the fractional approach are studied. New insight is provided and guidelines are given to attain tighter control over the number of the closed-loop eigenvalues and the compensator order, thus avoiding unnecessarily high order controllers and computationally expensive calculations. The study is carried out using the results of Antsaklis (1986) to derive the closed-loop internal descriptions directly in terms of the proper, stable factorizations of the plant and the controller transfer matrices.