Gupta et al. [2] used a Randomized Response Technique (RRT) to propose several estimators for finite population variance of a sensitive study variable using auxiliary information. In this paper, we modify those estimators by using the more efficient form of RRT, namely, Optional Randomized Response Technique (ORRT). Performance of the proposed estimators is evaluated using a unified measure of respondent privacy and estimator efficiency. We also estimate the sensitivity level of the sensitive study variable.