Recent work on causal learning has investigated the possible role of generic priors in guiding human judgments of causal strength. One proposal has been that people have a preference for causes that are sparse and strong—i.e., few in number and individually strong (Lu et al., 2008). Sparse-and-strong priors predict that competition can be observed between candidate causes of the same polarity (i.e., generative or else preventive) even if they occur independently. For instance, the strength of a moderately strong cause should be underestimated when a strong cause is also present, relative to when a weaker cause is present. In previous work (Powell et al., 2013) we found such competition effects for causal setups involving multiple generative causes. Here we investigate whether analogous competition is found for strength judgments about multiple preventive causes. An experiment revealed that a cue competition effect is indeed observed for preventive causes; moreover, the effect appears to be more persistent (as the number of observations increases) than the corresponding effect observed for generative causes. These findings, which are consistent with predictions of a Bayesian learning model with sparse-and-strong priors, provide further evidence that a preference for parsimony guides inferences about causal strength.