Abstract: A mounting system for repeatedly attaching and detaching an optical sighting device having a sighting axis to and from a supporting base having a base axis without interfering with the alignment between the two axes when the sighting device is in place on the base. The system utilizes a plurality of precisely spaced locating points between the holder of the sighting device and the supporting base. It is highly precise, relatively simple in construction, and may be attached and detached without tools. The system finds particular but not exclusive utility for mounting a telescopic sight on a rifle or other firearm.