Raghavarao and Federer (1979) used the theory of balanced incomplete block designs to determine the structure of the questionnaires in their block total response technique (symmetric designs)! Block total response technique is one of these methods that were initially proposed by Smith et al. (1974). The proposed design for six sensitive questions has... Randomized response technique has decades old history! Warner (1965) is the founder of this technique. In this study, some new designs are explored for 3 to 6 sensitive questions given a maximum total number of 13 questions while extending the work of Smith and Street (2003) to estimate the proportion of population for 3 to 10 sensitive questions given a maximum total number of 25 questions. Smith and Street (2003) determined the best designs in terms of minimum variance; used to estimate the proportions of 3 to 6 sensitive questions using the block total response procedure given a maximum total number of 13 questions.