Two modification models of Christofides model are proposed to estimate the proportion of the persons with sensitive characteristic, such as addiction to drugs and other intoxicants, induced abortions, proneness to tax evasion, gambling habits, history of past involvement in crimes, … , etc. These models are sketched by using Truncated Binomial and Binomial Distributions respectively. The simulation technique is used to examine the relative efficiency of the estimator of the Christofides model to the estimators of the two modification models, and relative efficiency of the estimator of the first modification model to the estimator of the second modification model. The efficiency of the estimators of the two modification models relative to the Cramer/-Rao bound is examined. A general linear randomized response models are established with estimates and variances obtained through analogy with familiar linear regression models