<p>This paper addresses the challenge of estimating the population proportion of a sensitive attribute using Franklin’s randomized response model, which encompasses several existing randomized response models as special cases. We propose a novel extension that incorporates an additional correlated scrambling variable to improve the efficiency of Franklin’s single-response-per-respondent method. The resulting estimator is shown to be unbiased, with an accompanying unbiased estimator of its variance. Analytical comparisons demonstrate that the proposed estimator consistently outperforms existing methods in terms of efficiency. Simulation studies are conducted to examine 95% confidence interval coverage and the incidence of inadmissible (i.e., negative) estimates across varying sample sizes. A minimum sample size is identified that reliably ensures non-negative estimates in practice. Numerical illustrations and simulations highlight the degree of percent relative efficiency achieved. The findings confirm that the proposed estimator acts as a triple authenticator, offering advantages from three distinct perspectives: relative efficiency, admissibility of estimates, and confidence interval coverage.</p>