An invasive instrument for treating a vessel, which possibly includes secondary vessels, has a tip formed for the dissection of tissue at the distal end of a shaft to be introduced into the body, with at least one functional unit. The tip includes vessel receptacle means, arranged and formed such that, in the operating condition of the instrument, the functional unit of the shaft is kept clear, so that working on the vessel, a secondary vessel and/or on the surrounding tissue is possible using or by means of the functional unit and with the vessel receiving means the vessel can be fixed in a spatial position. The tip is movable relative to the shaft by means of a guide element and the tip is shiftable in axial direction, so that during the procedure a vessel arranged in the vessel receiving means can be spaced selectively from the functional unit.