A reclosable package is provided having a front wall and a rear wall joined at the bottom and sides and an open top containing a zipper. The zipper has a first profile and a second profile, each including interlocking members adapted to mate with each other. One profile has a flange secured to its associated wall at a location proximal a top end of that wall. The second profile has a flange portion secured to the other wall proximal a top end of that wall and to the first wall at a location below the location at which the first flange is secured to the first wall. A line of weakness extends along the second flange portion parallel to the profile interlocking member and between the two securing points.