  We explore several supersymmetric alternatives to explain predictions for the
cosmic ray positron excess. Light sneutrino or neutralino LSP's, and a
fine-tuned model designed to provide a delta-function input, can give adequate
statistical descriptions of the reported HEAT data if non-thermal production of
the relic cold dark matter density dominates and/or if ``boost factors''(that
could originate in uncertainties from propagation or local density
fluctuations) to increase the size of the signal are included. All the
descriptions can be tested at the Tevatron or LHC, and some in other WIMP
detecting experiments.
