The Recursive Jigsaw Reconstruction technique provides a powerful way to search for new physics in scenarios with multiple missing particles in the final state. By defining a specific input decay tree we demonstrate a new approach to search for supersymmetry in scenarios where the mass difference between the parent super-particles and the lightest supersymmetric daughter particles is small. Such scenarios are colloquially referred to as ``compressed". The imposition of this decay tree provides a clear way to define which objects are associated with an initial-state radiation system, and those which are candidate decay products of the supersymmetric system of particles. From this choice a set of variables emerge, providing a method to distinguish compressed signals from the pernicious standard model backgrounds. We introduce this new approach and demonstrate it's power through application to searches in several final states. We further touch on the applicability of the Recursive Jigsaw method in general to new physics searches where conventional kinematic discriminators break down.