In this study we aim to test behavioural models of complexity aversion. In this framework, complexity is defined as a function of the number of outcomes in a lottery. Using Bayesian inference techniques, we re-analyse data from a lottery-choice experiment. We quantitatively specify and estimate adaptive toolbox models of cognition, which we rigorously test against popular expectation-based models; modified to account for complexity aversion. We find that for the majority of the subjects, a toolbox model performs best both in-sample, and with regards to its predictive capacity out-of-sample, suggesting that individuals resort to heuristics in the presense of extreme complexity.