A noncompressive dewatering device generates air streams that can be used to remove water from cellulosic webs in an energy efficient manner. Further, a wet-pressed machine can be modified to economically produce low-density tissue with an energy/capital efficiency greater than that of the throughdrying process. For instance, a cellulosic web can be non-compressively dewatered from a post forming consistency to a consistency from about 25 percent to the water retention consistency by passing air through the web with an Energy Efficiency at least 10 percent greater than that achievable using vacuum dewatering at the same speed. In particular embodiments, the web may be non-compressively dewatering to a consistency of at least 70 percent of the water retention consistency using about 13 or less horsepower per inch of sheet width, or to a consistency of at least 80 percent of the water retention consistency using about 30 or less horsepower per inch of sheet width, both at a speed of 2500 feet per minute or greater.