This paper proposes an approach for assessing the stability of feedback interconnections where one element is a static slope-restricted nonlinearity and the other element is a linear system. The approach is based on the use of Zames-Falb multipliers where the dynamic portion of the multiplier is chosen as an externally positive noncausal transfer function. By restricting attention to a subset of these multipliers, a set of pure linear matrix inequality conditions is obtained which requires no initial parameterization by the user. A useful byproduct of using externally positive systems is that the results are applicable to nonodd slope restricted nonlinearities, which is not the case for all classes of Zames-Falb multipliers.