Abstract: A nipple system for bottle-feeding a baby, comprising a hollow, pliant nipple with a small aperture at one end and open at the other end and a one-way valve interior to the nipple for allowing a flow of liquid as the baby opens the valve by compressing the nipple. The valve is located in the nipple and preferably also pliant and integral therewith, dividing the nipple into two chambers, communicating through a passage in the valve. The valve may comprise a flap that opens the passage when the nipple is compressed and closes when the nipple is released, or may be a slotted diaphragm biased toward the bottle that opens when the nipple is compressed.