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.
