In self-reports, socially desirable responding threatens the validity of prevalence estimates for sensitive personal attitudes and behaviors. Indirect questioning techniques such as the crosswise model attempt to control for the influence of social desirability bias. The crosswise model has repeatedly been found to provide more valid prevalence estimates than direct questions. We investigated whether crosswise model estimates are also less susceptible to deliberate faking than direct questions. To this end, we investigated the effect of "fake good" instructions on responses to direct and crosswise model questions. In a sample of 1,946 university students, 12-month prevalence estimates for a sensitive road traffic behavior were higher and thus presumably more valid in the crosswise model than in a direct question. Moreover, "fake good" instructions severely impaired the validity of the direct questioning estimates, whereas the crosswise model estimates were unaffected by deliberate faking. Participants also reported higher levels of perceived confidentiality and a lower perceived ease of faking in the crosswise model compared to direct questions. Our results corroborate previous studies finding the crosswise model to be an effective tool for counteracting the detrimental effects of positive self-presentation in surveys on sensitive issues.