Abstract. This paper evaluates the power of a new scheme that generates search heuristics mechanically. This approach was presented and evaluated rst in the context of optimization in belief networks. In this paper we extend this work to Max-CSP. The approach involves extracting heuristics from a parameterized approximation scheme called MiniBucket elimination that allows controlled trade-o between computation and accuracy. The heuristics are used to guide Branch-and-Bound and Best-First search, whose performance are compared on a number of constraint problems. Our results demonstrate that both search schemes exploit the heuristics e ectively, permitting controlled trade-o between preprocessing for heuristic generation and search. These algorithms are compared with a state of the art complete algorithm as well as with the stochastic local search anytime approach, demonstrating superiority in some problem cases.