A large number of findings in survey research suggest that responses to sensitive questions are situational and can vary in relation to context. The methodological literature demonstrates that social desirability biases are less prevalent in self-administered surveys, particularly in Web surveys, when there is no interviewer and less risk of presenting oneself in an unfavorable light. Since there is a growing number of users of mobile Web browsers, we focused our study on the effects of different devices (PC or cell phone) in Web surveys on the respondents' willingness to report sensitive information. To reduce selection bias, we carried out a two-wave cross-over experiment using a volunteer online access-panel in Russia. Participants were asked to complete the questionnaire in both survey modes: PC and mobile Web survey. We hypothesized that features of mobile Web usage may affect response accuracy and lead to more socially desirable responses compared to the PC Web survey mode. We found significant differences in the reporting of alcohol consumption by mode, consistent with our hypothesis. But other sensitive questions did not show similar effects. We also found that the presence of familiar bystanders had an impact on the responses, while the presence of strangers did not have any significant effect in either survey mode. Contrary to expectations, we did not find evidence of a positive impact of completing the questionnaire at home and trust in data confidentiality on the level of reporting. These results could help survey practitioners to design and improve data quality in Web surveys completed on different devices. © European Survey Research Association.