The author compared high- and low-threshold discrete-state models of recognition memory in terms of their ability to account for confidence and response time (RT) data. The 2-high threshold (2HT), 1-low threshold (1LT), and 2-low threshold (2LT) models were clearly distinguished by the commonly observed inverted-U pattern whereby RTs are longer for low-confidence than high-confidence responses on both sides of the confidence scale (correct responses and errors). The 2HT model was able to match the RT-confidence relationship for correct responses, but it was unable to match the same relationship for errors. The 1LT model could not match the RT-confidence relationship for either correct responses or errors. Only the 2LT model was able to match the full pattern. The differences between models were driven by their fundamental assumptions about memory retrieval: only the 2-threshold models could produce an RT-confidence relationship by mixing relatively fast responses from a detection state with relatively slow responses from an uncertain ("guess") state, and only the 2LT model could do so for both correct and error responses because it allows misleading detection. Quantitative fits also showed that the 1LT model could not account for changes in confidence-rating distributions across memory-strength conditions, and thus this model performed substantially worse than the other two models even when RT data were not considered.