Out of the toolbox of survey methods for obtaining honest answers to sensitive issues, the method of randomized responses (RR) has proven to be the most effective one. So far, in applications of RR methods it has been assumed that they eliminate response biases. We investigate the validity of this assumption by applying multivariate RR models that allow for different types of response biases. Our data analyses show that RR methods do not eliminate response biases but that they can be modeled in informative ways: accounting for response biases leads to estimates that are at least twice the size of the estimates obtained when response biases are ignored.