The limits of the static state feedback u = Fx + Gv, with G not necessarily nonsingular, in altering the transmission pole structure of the linear system (x) over dot = Ax f Bu are studied. A necessary and sufficient condition for a list of polynomials to be the denominator polynomials of the Smith-McMillan form of the closed-loop transfer matrix (sl - A -BF)(-1)BG is established. The condition involves the calculation of the infimal set of the controllability indices that the system can attain through feedback while satisfying the Rosenbrock inequalities.