A flash and sound suppressor for a firearm includes a housing with an inlet nozzle, and an end cap, with plural baffles between them, each having a central hole and a radial gap between the baffle and the housing. Between the flared inlet nozzle and the baffles is a first expansion chamber; between the baffles and the end cap is a second, smaller expansion chamber. The baffles are formed to divide and direct combustion gases between those that follow the bullet through the central hole and those that flow through the radial gap where they are re-directed by the next baffle back across the axis of the housing. The changing orientation of the baffles controls that re-direction. The end cap has an inner, toroidal surface formed to improve mixing in the second expansion chamber, and an outer surface that improves radial gas dispersion and separation.