A number of algorithms have recently been proposed that use iterative improvement (a form of hill-climbing) to solve constraint satisfaction problems. These techniques have had dramatic success on certain problems. However, one factor limiting their wider application is the possibility of getting stuck at non-solution local minima. In this paper we describe an iterative improvement algorithm, called Breakout, that can escape from local minima. We present empirical evidence that this method is very effective in cases where previous approaches have difficulty. Although Breakout is not, theoretically complete, in practice it appears to almost always find solutions ,for solvable problems. We prove that an idealized (but less efficient) version of the algorithm is complete.