What is the best way of discovering the underlying structure of a causal system composed of multiple variables? One prominent idea is that learners should manipulate each candidate variable in isolation to avoid confounds (sometimes known as the "Control of Variables" or CV strategy). We demonstrate that CV is not always the most efficient method for learning. Using an optimal actor model which aims to minimize the average number of tests, we show that when a causal system is sparse (i.e., when the outcome of interest has few or even just one actual cause among the candidate variables) it is more efficient to test multiple variables at once. Across a series of behavioral experiments, we then show that people are sensitive to causal sparsity and adapt their strategies accordingly. When interacting with a non-sparse causal system (high proportion of actual causes among candidate variables), they use a CV strategy, changing one variable at a time. When interacting with a sparse causal system they are more likely to test multiple variables at once. However, we also find that people sometimes use a CV strategy even when a system is sparse.