A mouthpiece for a woodwind instrument, such as a saxophone has a tubular body, with a front and a rear portion, each having a respective passage. The front portion has an opening that is at least partially covered by a reed. The front passage is wider then the opening. The front passage also has a bottom wall that descends toward the rear portion. The bottom wall has three zones, including a first zone disposed at a shallow angle with respect to the reed, a second zone with sharper angle then the first, and an end zone. The resulting mouthpiece generates smoother and fuller sounds then the prior art mouthpieces while at the same time projecting sounds more effective.