Anaphora resolution (coreference) systems designed for theCONLL2012 dataset typically cannot handle key aspects of the full anaphoraresolution task such as the identification of singletons and of certain types of non-referring expressions (e.g., expletives), as these aspectsare not annotated in that corpus. However, the recently releasedCRAC2018 Shared Task and Phrase Detectives (PD) datasets can nowbe used for that purpose. In this paper, we introduce an architecture to simultaneously identify non-referring expressions (includingexpletives, predicativeNPs, and other types) and build coreference chains, including singletons. Our cluster-ranking system uses anattention mechanism to determine the relative importance of the mentions in the same cluster. Additional classifiers are used to identifysingletons and non-referring markables. Our contributions are as follows. First of all, we report the first result on theCRACdata usingsystem mentions; our result is 5.8% better than the shared task baseline system, which used gold mentions. Our system also outperformsthe best-reported system onPDby up to 5.3%. Second, we demonstrate that the availability of singleton clusters and non-referringexpressions can lead to substantially improved performance on non-singleton clusters as well. Third, we show that despite our model notbeing designed specifically for theCONLLdata, it achieves a very competitive result