Simple modifications to the representation of the bounded real lemma (BRL) in the linear continuous time-invariant case are introduced. These modifications reduce the overdesign that occurs in the analysis and the design of systems with polytopic-type uncertainties. A different Lyapuno F function accompanies each of the vertices of the uncertainty polytope, thus eliminating the need for quadratic stability or stabilizability. The advantages of these new representations are demonstrated by way of two examples.