A dunnage conversion machine (10) and method for providing strips of dunnage that better fill a void in a container are characterized by means (24) for separately guiding at least two sheets of stock material (14 and 16) to respective laterally-disposed regions of an inlet (20) to a conversion assembly (40) such that one sheet does not wrap around another sheet, and means (12) for converting the sheets into strips of dunnage that can readily separate and follow separate paths.