Methods for creating multi-layered incrementally-stretched and incrementally-laminated bags with increased or maintained strength are described herein. An increased level of strength is achieved by bonding adjacent layers of a multi-layer film together in a manner that the bond strength of the laminated layers is less than a strength of a weakest tear resistance of the individual first and second film layers. The inventors have surprisingly found that such a configuration of light bonding provides increased and unexpected strength properties to the multi-layer film as compared to a monolayer film of equal thickness or a multi-layer film in which the plurality of layers are tightly bonded together.