Experiments on choice under risk typically involve multiple decisions by individual subjects. The choice of mechanism for selecting decision(s) for payoff is an essential design feature that is often driven by appeal to the isolation hypothesis or the independence axiom. We report two experiments with 710 subjects. Experiment 1 provides the first simple test of the isolation hypothesis. Experiment 2 is a crossed design with six payoff mechanisms and five lottery pairs that can elicit four paradoxes for the independence axiom and dual independence axiom. The crossed design discriminates between: (a) behavioral deviations from postulated properties of payoff mechanisms; and (b) behavioral deviations from theoretical implications of alternative decision theories. Experiment 2 provides tests of the isolation hypothesis and four paradoxes. It also provides data for tests for portfolio effect, wealth effect, reduction, adding up, and cross-task contamination. Data from Experiment 2 suggest that a new mechanism introduced herein may be less biased than random selection of one decision for payoff.