Our main goal in the present set of studies was to re-visit the question whether people are capable of inducing causal models from covariation data alone without further cues, such as temporal order. In the literature there has been a debate between bottom-up and top-down learning theories in causal learning. Whereas top-down theorists claim that in structure induction, covariation information plays none or only a secondary role, bottom-up theories, such as causal Bayes net theory, assert that people are capable of inducing structure from conditional dependence and independence information alone. Our three experiments suggest that both positions are wrong. In simple three-variable domains people are indeed often capable of reliably picking the right model. However, this can be achieved by simple heuristics that do not require complex statistics.