The RR methods are used to collect data relating to highly stigmatizing characteristics that are not generally available through direct surveys. However, such methods are not totally satisfactory. They are subjected to certain limitations, such as a lack of reproducibility, a high cost, and being time-consuming. Respondents very often suspect randomization devices and feel there might be some hidden trick in the randomization process through which their secrecy might be somehow revealed. Several alternative methods have been proposed in the literature to overcome such difficulties. The methods include the item count technique (ICT), the item sum technique (IST), the non-randomized response (NRR) method, the parallel method, the hidden sensitivity model, and the three-card method. Details of the proposed techniques, along with their theoretical results, have been presented in this chapter. Bayesian methods for analyzing sensitive questions for the NRR models have also been proposed.