This paper considers the problem of finding necessary and sufficient conditions for stabilizing the linear systemx= Fx+Guby means of feedback control laws u=Kxmeasuring as few components ofxas possible. Easily computable conditions are given which insure that a given component ofxmay 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.