  Most experiments that search for direct interactions of WIMP dark matter with
a target can distinguish the dominant electronrecoil background from the
nuclear recoil signal, based on some discrimination parameter. An acceptance
region is defined inthe parameter space spanned by the recoil energy and this
discrimination parameter. In the absence of a clear signal in thisregion, a
limit is calculated on the dark matter scattering cross section. Here, an
algorithm is presented that allows to define the acceptance region a priori
such that the experiment has the best sensitivity. This is achieved through
optimized acceptance regions for each WIMP model and WIMP mass that is to be
probed. Using recent data from the CRESST-II experiment as anexample, it is
shown that resulting limits can be substantially stronger than those from a
conventional acceptance region. In an experiment with a segmented target, the
algorithm developed here can yield different acceptance regions for the
individual subdetectors. Hence, it is shown how to combine the data
consistently within the usual Maximum Gap or Optimum Interval framework.

Instrumentation and Methods for Astrophysics