  We describe a new approach to the rare-event Monte Carlo sampling problem.
This technique utilizes a symmetrization strategy to create probability
distributions that are more highly connected and thus more easily sampled than
their original, potentially sparse counterparts. After discussing the formal
outline of the approach and devising techniques for its practical
implementation, we illustrate the utility of the technique with a series of
numerical applications to Lennard-Jones clusters of varying complexity and
rare-event character.
