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We consider the MAX-2-SAT problem on d-degenerate formulas. This class of 2-CNFs is a generalization of 2-CNFs of bounded tree width. We first show that the class of d-degenerate formulas is very broad, since random formulas can be shown to be d-degenerate for an appropriate d. Then we test several heuristic algorithms on random d-degenerate formulas and compare results against similar tests on regular random 2-CNFs. Finally, we model the performance of one of these algorithms, the greedy one, on both random and random d-degenerate formulas by systems of differential equations.