A bag has a recloseable fastener, a bottom and, for each side, a flap. The flap has side edges that are sealed to side edges of the bag, the flap being sized and dimensioned such that the flap lies flush against the side of the bag except when stretched or drawn apart therefrom, the flap being disposed intermediate the recloseable fastener and the bottom. The fastener is adapted such that the amount of force necessary to separate the components, when such force is applied to interiors of the walls at a position between the fastener and the bottom and adjacent the fastener, is greatly exceed by the amount of force necessary to separate the components: when such force is applied to the walls adjacent the upper edge; and when such force is applied to the free edges of the flaps.