Methods and devices are provided for efficient low power density endoluminal treatment of veins. Devices emit energy radially from an optical fiber with two or more emitting portions at its distal region. for 360° radial (circumferential) emission of vein walls. Emitting sections comprise a fiber with a truncated cone attached to a short conically-tipped fiber at the distal end. The fiber segments are butt-coupled or glued, and then laterally fused to the protective glass dome/cap. Laser power is substantially entirely absorbed within a fraction of the blood vessel wall to achieve blood vessel closure. Wavelengths including 980 nm, 1470 nm and 1950 nm are used which are substantially absorbed within the first third of a blood vessel wall. Consequently, a local anesthetic along the treated blood vessel is substantially avoided. Due to a fiber devices multiple emission points, withdrawal speed can be increased, and/or emitted energy levels can be set at minimum values.
