An exhaust discharge system and method of assembling is disclosed. The exhaust discharge system may comprises an ejector tube and an exhaust stack. The ejector tube includes an outlet having an outlet cross-section. The ejector tube is configured to convey treated exhaust to the outlet. The outlet cross-section is oriented at an outlet angle to a first horizontal plane. The exhaust stack includes a first conduit and a second conduit. The second conduit includes an exit port. The exit-port cross-section is oblong in shape.