  We demonstrate that some of the suggested five supergravity points for study
at the LHC could be approximately derived from perturbative string theories or
M-theory, but that charge and colour breaking minima would result. As a pilot
study, we then analyse a perturbative string model with non-universal soft
masses that are optimised in order to avoid global charge and colour breaking
minima. By combining measurements of up to six kinematic edges from squark
decay chains with data from a new kinematic variable, designed to improve
slepton mass measurements, we demonstrate that a typical LHC experiment will be
able to determine squark, slepton and neutralino masses with an accuracy
sufficient to permit an optimised model to be distinguished from a similar
standard SUGRA point. The technique thus generalizes SUSY searches at the LHC.
