A dunnage conversion machine (36) converts a sheet stock material into a dunnage product that is relatively thicker and less dense than the stock material, but is relatively thin and sufficiently flexible to function as a protective wrap. The conversion machine includes a feed mechanism (40) that advances a sheet stock material therethrough and a connecting mechanism (42) downstream of the feed mechanism. The connecting mechanism retards the passage of the sheet stock material therethrough by feeding the stock material therethrough at a slower rate than the feed mechanism feeds the stock material to the connecting mechanism. This causes the stock material to randomly crumple in a longitudinal space between the feed mechanism and the connecting mechanism. The connecting mechanism connects multiple overlapping layers of sheet stock material together as they pass therethrough, including connecting at least one crumpled sheet to one side of one other sheet.