A branch sleeve adapted to carry out a crimping process around mutually parallel electrically conductive conductor sections. The sleeve includes a first groove-shaped recess which connects with a second groove-shaped recess and with an open part that extends between the recesses. The first recess is adapted to freely embrace or surround a first conductor section, and the second recess is adapted to freely embrace or surround a second conductor section, wherein each of the recesses has an opening area which conforms with and exceeds the largest conductor-section area, for which the sleeve is dimensioned. The sleeve has a cross-sectional shape in the form of a stylized digit “three.” The distribution of material around the recesses of the branch sleeve, or a so-called 3-sleeve, and the form and orientation of the recesses, are mutually adapted to create reducing gatherings of material inter alia adjacent to and at a small distance from said open part, and increasing gatherings of material at the leg parts.