The random preference, Fechner (or ‘white noise’), and constant error (or ‘tremble’) models of stochastic choice under risk are compared. Various combinations of these approaches are used with expected utility and rank-dependent theory. The resulting models are estimated in a random effects framework using experimental data from two samples of 46 subjects who each faced 90 pairwise choice problems. The best fitting model uses the random preference approach with a tremble mechanism, in conjunction with rank-dependent theory. As subjects gain experience, trembles become less frequent and there is less deviation from behaviour consistent with expected utility theory.