We present an ILP-based model of zero anaphora detection and resolution that builds on the joint determination of anaphoricity and coreference model proposed by Denis and Baldridge (2007), but revises it and extends it into a three-way ILP problem also incorporating subject detection. We show that this new model outperforms several baselines and competing models, as well as a direct translation of the Denis / Baldridge model, for both Italian and Japanese zero anaphora. We incorporate our model in complete anaphoric resolvers for both Italian and Japanese, showing that our approach leads to improved performance also when not used in isolation, provided that separate classifiers are used for zeros and for explicitly realized anaphors.