The pole placement problem is studied in a frequency domain setting in which it is desired to define a feedback compensator which will simultaneously stabilize the system and place the poles of the resultant input-output gain at the zeros of a prescribed Hurwitz polynomial q(s). In tho single variate case this may be achieved if and only if o(q)≥ II(p)— δ where o(q) is the order of q(s), II(p) is the total number of RHP poles and zeros of the plant, and 8 is either 1 or 0 ; while in the multivariate case similar, but only partial, numerical results are obtained. Moreover, whon these inequalities are satisfied a complete parameterization of the required set of compensators is obtained.