We present a method that checks Query Containment for queries with negated IDB predicates. Existing methods either deal only with restricted cases of negation or do not check actually containment but uniform containment, which is a sufficient but not necessary condition for containment. Additionally, our queries may also contain equality, inequality and order comparisons. The generality of our approach allows our method to deal straightforwardly with query containment under constraints. Our method is sound and complete both for success and for failure and we characterize the databases where these properties hold. We also state the class of queries that can be decided by our method.