A pouch having a flap and a closure system featuring a face fastener attached to the front wall of the pouch body, and a mating flap fastener as part of the flap. One fastener of the closure system is a loop fastener component carrying a field of hook-engageable fibers. The other fastener of the closure system is a hook fastener component with an array of hooks. A significant majority of the hooks are oriented such that their heads point in a common lateral direction. The flap is elastically stretchable by pulling on its free edge, such that the flap maintains the loop fastener component securely engaged to the hook fastener component when under tension, and such that stretching the flap reduces engagement between the loop fastener component and the hook fastener component.
