In this article we present two mixed Randomized Response Models (RRM) which may be considered improvements over Kim and Warde (2005) mixed RRM. Relative efficiencies of proposed Models relative to Kim and Warde (2005) mixed RRM is studied in simple random sampling with replacement (SRSWR) as well as in stratified random sampling. The proposed models are seen to perform well in terms of variance at equal level of protection against privacy in the SRSWR and stratified random sampling.