Mounting unit for a press fitting, having: - a substantially cylindrical press sleeve with a pressing region, wherein the press sleeve has a predetermined external diameter d 3 with a predetermined tolerance range; and - a stop ring which is fixed at a first axial end of the press sleeve and delimits the pressing region in an axial direction of the press sleeve, wherein - the stop ring has a substantially cylindrical inner contour with projecting first regions and second regions which are recessed relative to the first regions, - a clear internal diameter d 1 between the first regions is smaller than the predetermined external diameter d 3, less a negative tolerance, so that the first regions of the stop ring engage in a clamping manner around an outer contour of the press sleeve, and - a clear internal diameter d 2 between the second regions is greater than the predetermined external diameter d 3, plus a positive tolerance, so that the second regions of the stop ring are located at a distance from the outer contour of the press sleeve; - wherein the predetermined tolerance range is at least 0.2 mm and in particular approximately 1% of a diameter of a pipe to be connected to the press fitting; - the clear internal diameter d 1 between the first regions is approximately 0.5% and/or at least 0.1 mm smaller than the predetermined external diameter d 3, less the negative tolerance; and - the clear internal diameter d 2 between the second regions is approximately 0.5% and/or at least 0.1 mm greater than the predetermined external diameter d 3, plus the positive tolerance. - a substantially cylindrical press sleeve with a pressing region, wherein the press sleeve has a predetermined external diameter d 3 with a predetermined tolerance range; and - a stop ring which is fixed at a first axial end of the press sleeve and delimits the pressing region in an axial direction of the press sleeve, wherein - the stop ring has a substantially cylindrical inner contour with projecting first regions and second regions which are recessed relative to the first regions, - a clear internal diameter d 1 between the first regions is smaller than the predetermined external diameter d 3, less a negative tolerance, so that the first regions of the stop ring engage in a clamping manner around an outer contour of the press sleeve, and - a clear internal diameter d 2 between the second regions is greater than the predetermined external diameter d 3, plus a positive tolerance, so that the second regions of the stop ring are located at a distance from the outer contour of the press sleeve; - the stop ring has a substantially cylindrical inner contour with projecting first regions and second regions which are recessed relative to the first regions, - a clear internal diameter d 1 between the first regions is smaller than the predetermined external diameter d 3, less a negative tolerance, so that the first regions of the stop ring engage in a clamping manner around an outer contour of the press sleeve, and - a clear internal diameter d 2 between the second regions is greater than the predetermined external diameter d 3, plus a positive tolerance, so that the second regions of the stop ring are located at a distance from the outer contour of the press sleeve; - wherein the predetermined tolerance range is at least 0.2 mm and in particular approximately 1% of a diameter of a pipe to be connected to the press fitting; - the clear internal diameter d 1 between the first regions is approximately 0.5% and/or at least 0.1 mm smaller than the predetermined external diameter d 3, less the negative tolerance; and - the clear internal diameter d 2 between the second regions is approximately 0.5% and/or at least 0.1 mm greater than the predetermined external diameter d 3, plus the positive tolerance.