An apparatus for manufacturing a thermal and/or acoustic insulation product based on mineral wool, including: a first line for production of first mineral fibers, including at least one fiberizing member; a second line for production of second mineral fibers, including at least one fiberizing member and a cross-lapping device; and a cross-lapping device configured to deposit the second mineral fibers onto the first mineral fibers by cross-lapping. The apparatus can manufacture a thermal and/or acoustic insulation product with improved thermal and/or acoustic properties.