Recently, sensory threshold concepts have been expanded to include affective perceptions of foods and beverages, especially measures of product rejection; however, each threshold interpretation depends largely on the methodology employed. By substituting cricket powder for whole-wheat flour in snack crackers (0%, 5%, 10%, 15%, and 20%), we proposed modifications to two existing threshold methodologies: a modified consumer rejection threshold (M-CRT) using a 2-alternative choice (2-AC) preference test with “no preference” option; and a modified hedonic rejection threshold (M-HRT) based on less-than-neutral hedonic scores according to a one-sample t-test. We also proposed two new concepts: a rejection tolerance threshold (RTT) and an associated rejection range (RR), based on a binomial acceptability question and a probit regression model. These new methods provide more realistic interpretations of rejection-type thresholds based on user-defined allowable rejection levels, or “rejection tolerance” (for RTT), and a model-derived stimulus range (RR) to capture the rejection level of interest while providing flexibility for product formulation. All thresholds were investigated separately for color, flavor, texture and overall perception, elucidating differential sensorial effects of our novel ingredient on the food matrix. We suggest that conducting all demonstrated techniques in a single testing session gives a more expansive view of rejection thresholds while requiring minimal additional resources.