The availability of quality information in bug reports that are created daily by software users is key to rapidly fixing software faults. Improving incomplete or deficient bug reports, which are numerous in many popular and actively developed open source software projects, can make software maintenance more effective and improve software quality. In this paper, we propose a system that addresses the problem of bug report incompleteness by automatically posing follow-up questions, intended to elicit answers that add value and provide missing information to a bug report. Our system is based on selecting follow-up questions from a large corpus of already posted follow-up questions on GitHub. To estimate the best follow-up question for a specific deficient bug report we combine two metrics based on: 1) the compatibility of a follow-up question to a specific bug report; and 2) the utility the expected answer to the follow-up question would provide to the deficient bug report. Evaluation of our system, based on a manually annotated held-out data set, indicates improved performance over a set of simple and ablation baselines. A survey of software developers confirms the held-out set evaluation result that about half of the selected follow-up questions are considered valid. The survey also indicates that the valid follow-up questions are useful and can provide new information to a bug report most of the time, and are specific to a bug report some of the time.