A function f : { 0 , 1 , 2 , L , a } n → R is said to be uncorrelated if Prob [ f ( x ) ≤ u ] = G ( u ) . This paper studies the effectiveness of simulated annealing as a strategy for optimizing uncorrelated functions. A recurrence relation expressing the effectiveness of the algorithm in terms of the function G is derived. Surprising numerical results are obtained, to the effect that for certain parametrized families of functions { G c ,       c ∈ R } , where c represents the “steepness” of the curve G ′ ( u ) , the effectiveness of simulated annealing increases steadily with c These results suggest that on the average annealing is effective whenever most points have very small objective function values, but a few points have very large objective function values.