We prove a new outer bound to the capacity region of a certain class of interference channels, and quantify the gap between it and the Han-Kobayashi inner bound. The new bound allows the recovery of the El Gamal-Costa characterization of the capacity region of certain deterministic interference channels, and also the recent characterization by Etkin, Tse and Wang of the capacity region of scalar Gaussian interference channels to within '1 bit'. Moreover, the new bound allows a straightforward generalization of the '1 bit' result to vector Gaussian interference channels.