A machine (24; 70) for converting plies (32, 34; 90, 92) of sheet stock material into a relatively lower density dunnage product, the machine (24; 70) comprising: a bunching assembly (30; 74) configured to randomly crumple each ply (32, 34; 90, 92) into a three-dimensional modified ply (36, 40; 94, 96), each ply (32, 34; 90, 92) being crumpled separately; a feeding assembly (42; 76) downstream of the bunching assembly (30; 74), the feeding assembly (42; 76) having a pair of opposed members (132, 134) arranged to advance the modified plies (36, 40; 94, 96) between the opposed members (132, 134) and to connect together longitudinally-extending overlapped portions of the modified plies (36, 40; 94, 96) to form a dunnage strip having a longitudinally-extending line of connection spaced from at least one edge of one of the modified plies (36, 40; 94, 96); characterised in that the bunching assembly (30, 74) comprises at least two converging chutes (98, 99) that define the respective paths (100, 101) for each ply, wherein the at least two converging chutes (98, 99) comprise an upper chute and a lower chute, each comprise an upper wall (111, 109) and a lower wall (113, 107), each lower wall (113, 107) being disposed opposite a respective upper wall (111, 109), the upper chute further including a diverter extending at least partially along the upper wall and the lower chute further including a diverter extending at least partially along the lower wall, whereby the diverters (77, 78) are opposed to one another, are disposed upstream of the opposed members (132, 134) and have a shape suitable for urging the sheet material in respective plies (32, 34; 90, 92) generally outward, thereby encouraging separation and minimizing overlap of free edges of the plies (32, 34; 90, 92) advancing along respective separate paths (100, 101). a bunching assembly (30; 74) configured to randomly crumple each ply (32, 34; 90, 92) into a three-dimensional modified ply (36, 40; 94, 96), each ply (32, 34; 90, 92) being crumpled separately; a feeding assembly (42; 76) downstream of the bunching assembly (30; 74), the feeding assembly (42; 76) having a pair of opposed members (132, 134) arranged to advance the modified plies (36, 40; 94, 96) between the opposed members (132, 134) and to connect together longitudinally-extending overlapped portions of the modified plies (36, 40; 94, 96) to form a dunnage strip having a longitudinally-extending line of connection spaced from at least one edge of one of the modified plies (36, 40; 94, 96); characterised in that the bunching assembly (30, 74) comprises at least two converging chutes (98, 99) that define the respective paths (100, 101) for each ply, wherein the at least two converging chutes (98, 99) comprise an upper chute and a lower chute, each comprise an upper wall (111, 109) and a lower wall (113, 107), each lower wall (113, 107) being disposed opposite a respective upper wall (111, 109), the upper chute further including a diverter extending at least partially along the upper wall and the lower chute further including a diverter extending at least partially along the lower wall, whereby the diverters (77, 78) are opposed to one another, are disposed upstream of the opposed members (132, 134) and have a shape suitable for urging the sheet material in respective plies (32, 34; 90, 92) generally outward, thereby encouraging separation and minimizing overlap of free edges of the plies (32, 34; 90, 92) advancing along respective separate paths (100, 101).