We generalize propositional analytic tableaux for classical and many{valued logics to constraint tableaux. W e s h o w that this technique provides a new translation from deduction into integer programming. The main advantages are (i) an e cient satisability c hecking procedure for classical and, for the rst time, for a wide range of many{valued, including in nitely{valued propositional logics (ii) a new point of view on classifying complexity o f m a n y{valued logics (iii) easy NP{containment proofs for many{valued logics.