The Oxford Thesaurus An A-Z Dictionary of Synonyms - undulyadv.

1) disproportionately, excessively, overly, unnecessarily, inordinately, unreasonably, irrationally, unjustifiably, improperly, inappropriately: He claimed that he was being unduly harassed by the police. 2) immoderately, lavishly, profusely, extravagantly: Don't be unduly generous in tipping our waiter - he did spill the soup in your lap.