The min-conflict heuristic (Minton et al. 1992) has been introduced into backtracking algorithms and iterative improvement algorithms as a powerful heuristic for solving constraint satisfaction problems. Backtracking algorithms become inefficient when a bad partial solution is constructed, since an exhaustive search is required for revising the bad decision. On the other hand, iterative improvement algorithms do not construct a consistent partial solution and can revise a bad decision without exhaustive search. However, most of the powerful heuristics obtained through the long history of constraint satisfaction studies (e.g., forward checking (Haralick and Elliot 1980)) presuppose the existence of a consistent partial solution. Therefore, these heuristics can not be applied to iterative improvement algorithms. Furthermore, these algorithms are not theoretically complete. In this paper, a new algorithm called weak-commitment search which utilizes the min-conflict heuristic is developed. This algorithm removes the drawbacks of backtracking algorithms and iterative improvement algorithms, i.e., the algorithm can revise bad decisions without exhaustive search, the completeness of the algorithm is guaranteed, and various heuristics can be introduced since a consistent partial solution is constructed. The experimental results on various example problems show that this algorithm is 3 to 10 times more efficient than other algorithms.