Most, if not all forms of ellipsis (e.g., 'so does Mary') are similar to reading comprehension questions ('what does Mary do'), in that in order to resolve them, we need to identify an appropriate text span in the preceding discourse. Following this observation, we present an alternative approach for English ellipsis resolution relying on architectures developed for question answering (QA). We present both single-task models, and joint models trained on auxiliary QA and coreference resolution datasets, clearly outperforming the current state of the art for Sluice Ellipsis (from 70.00 to 86.01 F₁) and Verb Phrase Ellipsis (from 72.89 to 78.66 F₁).