An apparatus and method for engaging and transferring a discrete part having a varying thickness to a substrate web. The apparatus includes one or more transfer assemblies and a web conveyor supporting the substrate web. Each transfer assembly includes a carrier member adapted to engage and transport the discrete part. One of the carrier member and the web conveyor includes a recessed portion for receiving portions of the discrete part that are relatively thicker than other portions of the discrete part, thereby ensuring more uniform contact between the discrete part and the web substrate.