This paper considers the problem of finding necessary and sufficient conditions for stabilizing the linear system x = Fx+Gu by means of feedback control laws u=Kx measuring as few components of x as possible. Easily computable conditions are given which insure that a given component of x may be eliminated from a stabilizing law (sufficiency), as well as simple conditions which must bo satisfied if a given component is to be so eliminated. Unfortunately, these conditions are not one and the same but numerical examples are given to demonstrate their utility none the less.