Scholars increasingly rely on indirect questioning techniques to reduce social desirability bias and item nonresponse for sensitive survey questions. The major drawback of these approaches, however, is their inefficiency relative to direct questioning. We show how to improve the statistical analysis of the list experiment, randomized response technique, and endorsement experiment by exploiting auxiliary information on the sensitive trait. We apply the proposed methodology to survey experiments conducted among voters in a controversial antiabortion referendum held during the 2011 Mississippi General Election. By incorporating the official county-level election results, we obtain precinct- and individual-level estimates that are more accurate than standard indirect questioning estimates and occasionally even more efficient than direct questioning. Our simulation studies shed light on the conditions under which our approach can improve the efficiency and robustness of estimates based on indirect questioning techniques. Open-source software is available for implementing the proposed methodology.