A conversion assembly for a dunnage conversion machine includes both a downstream pair of rotatable members and an upstream pair of rotatable members upstream of the downstream rotatable members. The downstream rotatable members include a pair of gears, and each gear has a plurality of teeth and is rotatable about a respective axis. The gears are positioned so that the teeth of one gear are sequentially interlaced with the teeth of the other gear as the gears rotate. The upstream rotatable members include a pair of feed wheels, and the gears and the feed wheels define a path for a sheet stock material from between the upstream pair of feed wheels to between the downstream pair of gears. The rate at which the sheet stock material is advanced by the feed wheels is the same as the rate at which the sheet stock material is advanced by the gears.