An air-evacuable bag has a one-way valve therein having two layers of valve film, neither of which is the sidewall of the bag. By forming the one-way valve of smooth, double-layered valve film, unwanted air gaps caused by textured surfaces in the sidewalls of the bag are avoided, thereby minimizing air leakage back into an evacuated bag. A method for the manufacture of such air-evacuable bags incorporates a roll supplying a first valve film layer, a roll supplying a first sidewall layer, a roll supplying a second valve film layer, and a roll supplying a second sidewall layer. As the film coming off the first valve film layer roll passes the roll supplying the first sidewall layer, both the sidewall layer and first valve film layer move in close proximity to one another until the valve film is tacked to the first sidewall layer. The second film and second sidewall layer are processed simultaneously in a like manner, and all four layers are joined at a sealing station.