  The LHC has the potential not only to discover supersymmetry (SUSY), but also
to permit fairly precise measurements of at least a portion of the sparticle
spectrum. Proposed mass reconstruction methods rely upon either inverting
invariant mass endpoint expressions or upon solving systems of mass-shell
equations. These methodologies suffer from the weakness that one certain
specific sparticle decay chain is assumed to account for all the events in the
sample. Taking two examples of techniques utilizing mass-shell equations, it is
found that also applying the wedgebox technique allows for the isolation of a
purer event sample, thus avoiding errors, possibly catastrophic, due to
mistaken assumptions about the decay chains involved and simultaneously
improving accuracy. What is innovative is using endpoint measurements (via the
wedgebox technique) to obtain a more homogeneous, well-understood sample set
rather than just using said endpoints to constrain the values of the masses
(here found by the mass-shell technique). The fusion of different established
techniques in this manner represents a highly profitable option for LHC
experimentalists who will soon have data to analyze.
