  We present a method for optimising experimental cuts in order to place the
strongest constraints (upper limits) on theoretical signal models.
  The method relies only on signal and background expectations derived from
Monte-Carlo simulations, so no bias is introduced by looking at actual data,
for instance by setting a limit based on expected signal above the ``last
remaining data event.'' After discussing the concept of the ``average upper
limit,'' based on the expectation from an ensemble of repeated experiments with
no true signal, we show how the best model rejection potential is achieved by
optimising the cuts to minimise the ratio of this ``average upper limit'' to
the expected signal from the model. As an example, we use this technique to
determine the limit sensitivity of kilometre scale neutrino detectors to
extra-terrestrial neutrino fluxes from a variety of models, e.g. active
galaxies and gamma-ray bursts. We suggest that these model rejection potential
optimised limits be used as a standard method of comparing the sensitivity of
proposed neutrino detectors.
