A finishing tool of an end milling cutter can comprise: a chip-removing milling edge, which extends continuously with respect to the tool axis (A) over an axial length (L) on a circumferential surface (U), which is rotationally symmetrical about the tool axis, and removes workpiece chips from the workpiece surface at a radial chip-removing engagement depth (T to Tmax), and at least one non-cutting pressing ridge, which extends continuously axially with respect to the tool axis (A) over an axial length (L) on a circumferential surface which is rotationally symmetrical about the tool axis, is arranged following an associated milling edge by a pitch angle, and presses over its entire axial length (L), during the milling movement, at a radial non-cutting engagement depth (T or RS−RD) with respect to the tool axis into the workpiece surface machined by the associated milling edge, and smooths said workpiece surface.