Data from a risky choice experiment are used to estimate a fully parametric stochastic model of risky choice. As is usual with such analyses, Expected Utility Theory is rejected in favour of a form of Rank Dependent Theory. Then an estimate of the risk aversion parameter is deduced for each subject, and this is used to construct a measure of the “closeness to indifference'' of each subject in each choice problem. This measure is then used as an explanatory variable in a random effects model of decision time, with other explanatory variables being the complexity of the problem, the financial incentives, and the amount of experience accumulated at the time of performing the task. The most interesting finding is that significantly more effort is allocated to problems in which subjects are close to indifference. This presents us with another reason (in addition to statistical information considerations) why such tasks should play a prominent role in experiments.