A rain gutter system includes a back flashing, fastening clips, fasteners, a rain gutter and a reverse-curve shield. The back flashing overlaps existing flashing and has a crease at the bottom and the fastening clips have a groove that locates the fastening clips relative to the back flashing. The back wall of the rain gutter extends above and behind the bottom of the back flashing. The rain gutter and shield are anchored to the back flashing and fastening clips vertically and in the fore/aft direction, and can slide laterally. The front upper end of the rain gutter slopes up and back to improve debris shedding.