An uncreped tissue sheet having improved softness results from supplementally dewatering a wet web to a consistency of greater than about 30 percent using noncompressive dewatering techniques (30) prior to a differential speed transfer (37) and subsequent throughdrying (44). An air press (30) particularly well suited for providing the supplemental noncompressive dewatering incorporates side (80) and/or end seals (78) to minimize escape of pressurized fluid.
