Threshold models assumeJdiscrete sensory states, which are related to responses by a probabilistic response rule. The paper discusses how we can refute threshold models withJsmall without imposinga prioriconstraints on the response rule. An argument due to Krantz is extended and applied to a sinusoid‐in‐noise detection task with randomly varying signal strengths. When five subjects are tested in this task, it is shown thatJneeds to be at least 3 for four subjects and at least 4 for