Tolerance for blood transfusion risks is very low, as evidenced by the implementation of expensive blood tests and the rejection of gay men as blood donors. Is this low risk tolerance supported by the precautionary principle, as defenders of such policies claim? We discuss three constraints on applying (any version of) the precautionary principle and show that respecting these implies tolerating certain risks. Consistency means that the precautionary principle cannot prescribe precautions that it must simultaneously forbid taking, considering the harms they might cause. Avoiding counterproductivity requires rejecting precautions that cause more harm than they prevent. Proportionality forbids taking precautions that are more harmful than adequate alternatives. When applying these constraints, we argue, attention should not be restricted to harms that are human caused or that affect human health or the environment. Tolerating transfusion risks can be justified if available precautions have serious side effects, such as high social or economic costs.