This work offers ways of maximizing efficiency of randomized response technique for two sensitive characters. In order to maximize the efficiency, two models; simple and crossed models were considered under equal and unequal protections. It was discovered that as increases, the simple model with equal protection becomes more efficient than the crossed model with unequal protection. And as continues to increase, the simple model with equal protection becomes approximately equal to the crossed model with equal protection. It was also shown that model with equal protection is more efficient than that due to unequal protection for both simple and crossed models. Hence, to ensure better estimation of two sensitive characters at a time, there is need to allow for equal protection of the respondents on each of the characters of interest

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