The present invention relates to a recloseable package for a product comprising a pouch having a space therein for storing a product. The pouch is provided with a recloseable feature (30) on inside surfaces of its side walls or on one of its ends. A score line (50) is provided in one of the side walls or in a sheath disposed over the reclosable feature. The score line traces a path from above the recloseable feature at the edges of the pouch to below the recloseable feature between the edges.