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. The line of weakness is formed in the cusp of a V-shaped section formed in the second flange and a peel seal is provided above the line of weakness joining together the sides of the V-shaped section.