We analyze lottery-choice data in a way that separately estimates the effects of risk aversion and complexity aversion, and allows both of these to vary between individuals, and also to change with experience. The data is from an experiment in which 80 subjects engage in a sequence of 54 choices between pairs of lotteries. The lotteries always have the same expected value, but they differ in terms of variance and the level of complexity. Complexity is represented by the number of different outcomes in the lottery, and is either 1 (sure win), 3 (simple), 6 (complex) or 27 (very complex). A finite mixture random effects model is estimated which assumes that a proportion of the population are complexity neutral, and we find that around 32% of the population are complexity neutral. In those subjects who do react to complexity, there is 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 complexity neutral by the end of the experiment. Around 23% of subjects appear complexity loving. Some of these findings are consistent with switching patterns seen in the choice data. Complexity aversion is found to increase with age, and is found to be higher for non-UK students than for UK students.