A new method that uses information obtained not only from randomization device but also from direct question is introduced. The new maximum likelihood estimator is compared with those of Warner(1965) and Mangat(l994). For a choice of randomized device, we propose a choice depending on the sample size n and show that our estimator is more efficient than that of Mangat under the randomization device. The proposed procedure is extended to more general one which can be easily applied to some specific cases. Under the specified conditions, it is shown that the variance of this generalized estimator is smaller than that of Warner.