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.