A system, and associated components and methodology, having a dunnage supply with an outlet through which one or more crumpled strips are supplied, a positioning device that positions in juxtaposition portions of the one or more strips of dunnage, and a stapler for connecting the juxtaposed portions to hold them together. In a particular system, the system includes a converter that has a conversion assembly that converts a sheet stock material into a crumpled strip of dunnage and has an outlet through which the strip of dunnage is emitted. The system also includes a coiler that rolls the strip of dunnage into a coil, and a stapler that secures the trailing end portion of the strip of dunnage to at least the next-innermost portion of the strip in the coil by inserting a staple through the trailing end portion and the juxtaposed portion of the coiled strip.