We present a novel approach to automatically reformulating constraints defined as tables of allowed assignments to variables. Constraints of this form are common in a variety of settings. Specifically, we propose an approach in which a high arity table constraint is reformulated as a conjunction of lower arity constraints. The reformulation is logically equivalent to the original constraint. We demonstrate that by using functional dependencies from the field of database design such reformulations can be found. We apply the approach to the problem of generating explanations as minimal conflicts. We show that reformulations can be found that yield compact explanations of inconsistency by reducing both the number of variables required to explain inconsistency and the arity of the largest constraint involved in the explanation. We demonstrate our approach on real-world datasets with positive results. © 2008 Springer Science+Business Media, LLC.