Davidson's principle of the anomalousness of the mental was instrumental in discrediting once-popular versions of mind-brain reductionism. In this essay I argue that a novel account of intertheoretic reduction, which does not require the sort of cross-theoretic bridge laws that Davidson's principle rules out, allows a version of mind-brain reductionism which is immune from Davidson's challenge. In the final section, I address a second worry about reductionism, also based on Davidson's principle, that survives this response. I argue that new reductionists (...) should revise some significant details of the program, particularly the conception of theories, to circumvent this more potent Davidson-inspired worry. (shrink)