The article is devoted to the description and analysis of the "crosswise" and "triangular" models, pioneered in 2008 by Hong Kong statisticians Yu, Tian and Tang and belonging to the class of non-randomized survey techniques (NRRT), specifically designed to control the effects of social desirability and stimulate self-disclosure of respondents in sensitive surveys. Based on the results of foreign studies, the authors made an attempt to evaluate the possibilities of these models for obtaining sincere answers from the respondents. The paper describes design features, question-answer logic and statistical foundations of both models under study. Methods for calculating a probabilistic estimate of the prevalence of the studied sensitive behavior are presented. The results of empirical tests are offered making it possible to judge the validity of the two techniques. The advantages of the crosswise and triangular models compared to the Warner RRT technique and the self-report method are shown, consisting in high validity, good performance by both respondents and interviewers, as well as methodological versatility. The most important shortcomings and limitations of survey techniques related to the respondents' non-compliance with the prescribed instructions and the subjective preferences of the interviewees in relation to certain response options are analyzed. The mechanism of the appearance of false-positive assessments that negatively affects the validity of the final data is revealed. Possible solutions to this problem are proposed. As a result of a comparative analysis of the two studied models, the authors come to the conclusion that the advantage in choosing between these two indirect techniques in terms of practical application remains with the crosswise model due to the symmetry of its question-answer design and more effective control of social desirability effects.