In social surveys on sensitive characteristics, optional randomized response models give the respondents the option to either report the true response or report the scrambled response. If any respondent finds that the question being asked does not feel sensitive, he/she reports the true response. In the existing variants of optional randomized response models, the researcher doesn’t know whether the respondent opted for the correct response or for a scrambled response. In practice, some of the respondents may have no problem in disclosing to the researcher that they are giving the true response and hence not opting for scrambling. This paper presents an alternative procedure to optional scrambling randomized response models, where each respondent has the choice whether or not to disclose to the researcher that he/she is giving the true response. Alternative modified versions of three existing scrambling randomized response models are presented. It is found that the efficiency of the quantitative randomized response models improves if the exact number of respondents who are opting for scrambling, is known to the researcher. Besides improvement in efficiency, the level of the respondent-privacy is the same as that of the existing models, thus resulting in an improvement in the overall quality of the existing models.