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Current end-to-end coreference resolution models combine detection of singleton mentions and antecedent linking into a single step. In contrast, singleton detection was often treated as a separate step in the pre-neural era. In this work, we show that separately parameterizing these two sub-tasks also benefits end-to-end neural coreference systems. Specifically, we add a singleton detector to the coarse-to-fine (C2F) coreference model, and design an anaphoricity-aware span embedding and singleton detection loss. Our method significantly improves model performance on OntoNotes and four additional datasets.