This is a rotary lamination press used to squeeze an adhesive coated sheet onto a substrate. It is designed for the lamination of sheets that are coated with wet adhesive or contact cement, but can also be used for the lamination of sheets using film adhesives. The laminating smoothing press has a fixed lower roller and a floating upper roll. The upper roll is designed to provide enough pressure to squeeze out bubbles and wrinkles trapped between the substrates, giving a high quality lamination. The nip pressure between the rolls is created by the weight of the upper roller. The pressure between the nip rolls is sufficient to squeeze air bubbles out of the layers of the lamination, but does not exert excessive pressure that would crush the flutes on corrugated or collapse foamcore board. The floating upper roll can follow variations in substrate thickness while maintaining consistent nip roll pressure. Both nip rolls are powered to provide positive pulling force and eliminate any slippage between the layers of the lamination.