  The lack of a new physics signal thus far at the Large Hadron Collider
motivates us to consider how to look for challenging final states, with large
Standard Model backgrounds and subtle kinematic features, such as cascade
decays with compressed spectra. Adopting a benchmark SUSY-like decay topology
with a four-body final state proceeding through a sequence of two-body decays
via intermediate resonances, we focus our attention on the kinematic variable
$\Delta_{4}$ which previously has been used to parameterize the boundary of the
allowed four-body phase space. We highlight the advantages of using
$\Delta_{4}$ as a discovery variable, and present an analysis suggesting that
the pairing of $\Delta_{4}$ with another invariant mass variable leads to a
significant improvement over more conventional variable choices and techniques.
