Traditional searches for R-parity conserving natural supersymmetry (SUSY) require large transverse mass and missing energy cuts to separate the signal from large backgrounds. SUSY models with compressed spectra inherently produce signal events with small amounts of missing energy that are hard to explore. We use this difficulty to motivate the construction of "deconstructed" transverse mass variables which are designed preserve information on both the norm and direction of the missing momentum. We demonstrate the effectiveness of these variables in searches for the pair production of supersymmetric top-quark partners which subsequently decay into a final state with an isolated lepton, jets and missing energy. We show that the use of deconstructed transverse mass variables extends the accessible compressed spectra parameter space beyond the region probed by traditional methods. The parameter space can further be expanded to neutralino masses that are larger than the difference between the stop and top masses. In addition, we also discuss how these variables allow for novel searches of single stop production, in order to directly probe unconstrained stealth stops in the small stop- and neutralino-mass regime. We also demonstrate the utility of these variables for generic gluino and stop searches in all-hadronic final states. Overall, we demonstrate that deconstructed transverse variables are essential to any search wanting to maximize signal separation from the background when the signal has undetected particles in the final state.

41 pages, 17 figures