We study the multiple minima problem for Lennard-Jones clustersusing an effective potential which is afunction of the mean position x̄ and fluctuation σ atfinite temperature. It is shown that this methodsmoothsthe potential energy hypersurface and facilitates the search for theglobal minimum. The method is appliedto small Lennard-Jones clusters from 2 to 19 atoms and is shown to giveaccurate results.