Consider the problem of identifying important factors influencing a response in a simulation experiment where the number of factors is large. When the direction of the effect of factors is known, the method of sequential bifurcation is effective for quickly removing non-influential factors. Though good, the method is not fully efficient in that not all the information available is fully utilized. We present a method based on a polytope construction that makes use of all available information and which is therefore more efficient. In this paper we focus on the deterministic case to highlight its theoretical foundation. The method can however be extended to the stochastic case. Numerical examples are given comparing the new method with sequential bifurcation showing its improved performance.