If Peter prevents Jack from catching a falling bottle that Mike knocked over, most people would think that Mike caused the spill to a greater degree than Peter. Cases of double prevention like these are famously inconsistent with the idea that causal judgments rely on counterfactual dependence; the spill wouldn't have happened if Mike hadn't knocked the bottle over or if Peter hadn't prevented Jack from catching the bottle. But newer counterfactual models are more flexible, and they assume that people imagine different counterfactuals in proportion with their perceived normality. Following recent work showing that these newer models can account for causal judgments in cases of double prevention, here we find that normality affects such judgments. Specifically, when the productive factor is normal and the double preventer is abnormal, we find that participants preferentially rate either the productive factor or the double preventer as more causal depending on the normality of the possible preventer. Contrary to standard interpretations, then, our results suggest that cases of double prevention are actually more problematic for competing theories of causal judgment than they are for counterfactual theories.