A squeeze bottle forces substantially all of the liquid to be dispensed toward a top of the bottle. A valving arrangement reduces or eliminates a likelihood of air contacting the liquid to be dispensed. A top cap has a nozzle with a one-way valve allowing liquid to leave a liquid bag. A bottom cap has a one-way valve allowing air to enter an airbag. The liquid bag and the airbag are positioned within a sealed third chamber. The liquid bag and the airbag have a controlled interaction within the sealed third chamber, which results in substantially complete emptying of the liquid bag by squeezing the bottle.