A muffler for automotive vehicles. The muffler includes a passageway, an inlet at one end of the passageway, and a single outlet or dual outlets at the passageway's other end. The portion of the muffler connected to the inlet is substantially untapered. The portion of the passageway connected to the outlet or outlets tapers from wide to narrow away from the inlet and toward the outlet or outlets. This tapered geometry results in a very appreciable reduction of heat transmitted from the muffler back to the engine, increases engine performance, and produces a pleasant, deep sound while the engine is running.