Back-up sights for use on a rifle configured with an optical sight aligned along a first sighting axis include a handguard or support carrying first and second attachment points that are substantially parallel with the central axis of the rifle's barrel but offset at a different angle than the first sighting axis. A back-up front sight and rear sight are carried on a back-up sight base, where the front sight and rear sight are aligned along a second sight axis that is offset, preferably, by one-eighth turn from the first sighting axis. When using the back-up sights, the user tilts or cants the rifle to one side, rotating the rifle one-eighth turn about the axis of the barrel's bore, to look down the second sighting axis, while aiming the rifle at the target.