An accessory for partially enclosing a shaft of an endoscope is disclosed. The accessory defines a first space for accommodating the shaft and a second space for defining a conduit along the shaft. An outer surface of the accessory around the first and second spaces is centered on a first longitudinal axis, and the first space is centered on a second longitudinal axis spaced relative to the first longitudinal axis. The first space is open to one side, so that the accessory only partially encloses the shaft when placed around it.
