This paper revisits the interference channels under strong interference and very strong interference, for both discrete memoryless and Gaussian channels. In particular, it is shown that for the classical definitions, while the conditions of strong interference for discrete and Gaussian cases coincide with each other, those of very strong interference are not consistent with each other in terms of mutual information inequalities. Based on this observation, a new class of discrete memoryless interference channels under very strong interference is introduced whose capacity region is characterized. This new class of channels is consistent with the Gaussian interference channel under very strong interference. Moreover, this new class of interference channels is not a subset of any existing classes of discrete memoryless interference channels with known capacity region.