Randomized response techniques (RRTs) are useful survey tools for estimating the prevalence of sensitive issues, such as the prevalence of doping in elite sports. One type of RRT, the unrelated question model (UQM), has become widely used because of its psychological acceptability for study participants and its favorable statistical properties. One drawback of this model, however, is that it does not allow for detecting cheaters--individuals who disobey the survey instructions and instead give self-protecting responses. In this article, we present refined versions of the UQM designed to detect the prevalence of cheating responses. We provide explicit formulas to calculate the parameters of these refined UQM versions and show how the empirical adequacy of these versions can be tested. The Appendices contain R-code for all necessary calculations.