Abstract: In this paper, we have suggested a family of estimators πˆW for estimating π, the proportion of population having sensitive category, under unrelated question randomized response model. It is shown that the suggested class of estimators πˆW of π is more efficient than Mangat et al.’s  estimator πˆ1. Since πˆW bases on the unknown scalar W, it has little practical utility. By replacing W in πˆW by its various estimated values, tww estimators πˆW(i), i=1,2, have been suggested for use in practice. Exact efficiency of πˆW(i) have been worked out numerically.