An improved method and device provides safe and efficient low power density endoluminal treatment of venous insufficiency and similar procedures. One such device emits pulsed or continuous energy radially from an optical fiber with two or more emitting portions at its distal region for 360° radial (circumferential) emission onto the vein. Each emitting section comprises at least one fiber with a truncated cone and a short fiber segment with a conical tip at the distal end of the fiber assembly. Geometrical dimensions of emitting sections, such as truncated cone diameter, fiber core diameter and length of final distal fiber segment can vary. In a preferred embodiment, the fiber and the short fiber segment are "butt-coupled" inside a glass dome and laterally fused to the protective glass dome. In another preferred embodiment, the truncated cone of the fiber is glued to the proximal end of the fiber segment, in another embodiment, the contact area is fused first, then, an outer tube is attached. Laser radiation is transmitted at a wavelength and power such that is it substantially entirely absorbed within a fraction of the blood vessel wall to sufficiently damage the intravascular endothelium and, in turn, achieve blood vessel closure. Exemplary wavelengths include, 980 nra, 1470 nm and 1950 nm. The need for a local anesthetic is substantially diminished compared to earlier products. The presence of multiple emission points, allows increased withdrawal speeds, and/or setting emitted energy levels at minimum values.Linvention concerne un procédé et un dispositif améliorés qui permettent un traitement endoluminal sûr et efficace de linsuffisance veineuse à faible éclairement énergétique et des protocoles similaires. Lun de ces dispositifs émet une énergie pulsée ou continue en direction radiale depuis une fibre optique avec deux portions émettrices ou davantage dans sa région distale pour une émission radiale à 360° (circonférentielle) sur la veine. Chaque section émettr
