Increasing carbon dioxide (CO2) in the atmosphere usually reduces Earth’s outgoing longwave radiation (OLR). The unusual case of Antarctica, where CO2 enhances OLR and implies a negative forcing, has previously been explained by the strong near-surface inversion or extremely low surface temperature. However, negative forcing can occasionally be found in the Arctic and tropics where neither of these explanations applies. Here, we examine the changes in infrared opacity from CO2 doubling in these low or negative forcing climate states, which shows the predominant role of the stratospheric contribution to the broadband forcing. Negative forcing in today’s climate demands a combination of strong negative forcing caused by a steep stratospheric temperature inversion and a weaker positive forcing in the atmospheric window, which can be caused by a low surface temperature or a strong high cloud masking effect. Contrary to conventional wisdom, the near-surface inversion has little impact on the forcing.