A package includes a container and a lid adapted to mate with a brim of the container. The lid closes a top opening in the container when mounted on the container. In a lid-coupling process, a product is discharged from an interior product-storage region formed in the container. The elastic top wall of the lid is moved along the container brim to establish a radially outwardly moving brim-wiping motion to cause substantially all of any spilled product located on the annular brim to be displaced and wiped off the container brim so that little, if any, spilled product remains on the container brim.