How can we elicit honest responses in surveys? Conjoint analysis has become a popular tool to address social desirability bias (SDB), or systematic survey misreporting on sensitive topics. However, there has been no direct evidence showing its suitability for this purpose. We propose a novel experimental design to identify conjoint analysis’s ability to mitigate SDB. Specifically, we compare a standard, fully randomized conjoint design against a partially randomized design where only the sensitive attribute is varied between the two profiles in each task. We also include a control condition to remove confounding due to the increased attention to the varying attribute under the partially randomized design. We implement this empirical strategy in two studies on attitudes about environmental conservation and preferences about congressional candidates. In both studies, our estimates indicate that the fully randomized conjoint design could reduce SDB for the average marginal component effect (AMCE) of the sensitive attribute by about two-thirds of the AMCE itself. Although encouraging, we caution that our results are exploratory and exhibit some sensitivity to alternative model specifications, suggesting the need for additional confirmatory evidence based on the proposed design.