This paper addresses the current state of coreference resolution evaluation, in which different measures (notably, MUC, B3, CEAF, and ACE-value) are applied in different studies. None of them is fully adequate, and their measures are not commensurate. We enumerate the desiderata for a coreference scoring measure, discuss the strong and weak points of the existing measures, and propose the BiLateral Assessment of Noun-Phrase Coreference, a variation of the Rand index created to suit the coreference task. The BiLateral Assessment of Noun-Phrase Coreference rewards both coreference and non-coreference links by averaging the F-scores of the two types, does not ignore singletons – the main problem with the MUC score – and does not inflate the score in their presence – a problem with the B3 and CEAF scores. In addition, its fine granularity is consistent over the whole range of scores and affords better discrimination between systems.