Warner's (1965) original randomized response technique for dichotomous data was extended by Abul-Ela, et al. (1967) to the case of a multinomial with t ≥ 3 groups, r of which are stigmatizing. A competing approach for estimating a multinomial via the randomized response technique is discussed by Warner (1971). Yet a third approach, for the multinomial is considered by Greenberg, et al. (1969) and is based on using an alternate independent question. Here we outline some alternative schemes for estimating the t group proportions when r < t −1, using only one sample. Their realizations for any sampled individual, constitute two-stage schemes. The second stage is conditional on the random individual's response in the first stage. In Section 1 we briefly summarize the three existing methods. Section 2 describes the new procedures and the resulting estimators. In Section 3 we identify the new schemes as special cases of Warner's (1971) general linear randomized response model thereby obtaining alternative estim...