In this paper, we establish a new outer bound to the capacity region of the Gaussian Z-interference channel and also characterize the capacity of two new classes of discrete memoryless interference channels. The latter is achieved by proving the optimality of the Han-Kobayashi inner bound via traditional converse proofs. The former is done by utilizing an outer bound, generally not computable for discrete interference channels, to derive a new outer bound for Gaussian Z-interference channels, and its computability is deduced by showing Gaussian extremality.