We analyze lottery-choice data in a way that separately estimates the effects of risk aversion and complexity aversion. Complexity is represented by the number of different outcomes in the lottery. A finite mixture random effects model is estimated which assumes that a proportion of the population are complexity-neutral. We find that around 33% of the population are complexity-neutral, around 50% complexity-averse, and the remaining 17% are complexity-loving. Subjects who do react to complexity appear to have a bias towards complexity aversion at the start of the experiment, but complexity aversion reduces with experience, to the extent that the average subject is (almost) complexity-neutral by the end of the experiment. Complexity aversion is found to increase with age and to be higher for non-UK students than for UK students. We also find some evidence that, when evaluating complex lotteries, subjects perceive probabilities in accordance with Prospective Reference Theory.