The paper reconsiders and compares some randomized response models in the light of the efficiency/protection criterion. The results show that, despite the assertion of the authors about the superiority of their methods, some procedures are perfectly equivalent to theWarner’s or the Simmons’models. Our work extends and generalizes the results of Bhargava and Singh [2002. On the efficiency comparison of certain randomized response strategies. Metrika 55, 191–197] and other authors. © 2006 Elsevier B.V. All rights reserved.