Electric dipole moments of nuclei, diamagnetic atoms, and certain molecules are induced by CPviolating nuclear forces. Naive dimensional analysis predicts these forces to be dominated by longrange one-pion-exchange processes, with short-range forces entering only at next-to-next-to-leading order in the chiral expansion. Based on renormalization arguments we argue that a consistent picture of CP -violating nuclear forces requires a leading-order short-distance operator contributing to 1 S0-3 P0 transitions, due to the attractive and singular nature of the strong tensor force in the 3 P0 channel. The short-distance operator leads to O(1) corrections to static and oscillating, relevant for axion searches, electric dipole moments. We discuss strategies how the finite part of the associated low-energy constant can be determined in the case of CP violation from the QCD θ term by the connection to charge-symmetry violation in nuclear systems.