An apparatus for treating a hollow anatomical structure, said apparatus comprising: an implant sized for insertion into said hollow anatomical structure, said implant being elongate wherein said implant has an axial dimension which is greater than its radial dimension, said implant having a distal section and a proximal section; implant comprising a plurality of loose, non-knit and non-woven fibers, each fiber having a number of bends along the length thereof, each bend having an angle such that when each fiber is compressed radially, the bend angle generally increases and the fiber has a greater axial length and a smaller radial width than when uncompressed, each of said fibers being formed from one or more bioabsorbable materials and having a denier of about 0.1 to about 10; said implant being radially compressible to facilitate insertion into said hollow anatomical structure, and said implant being expandable toward a radially larger, less radially dense elongate configuration, the expansion facilitated by a tendency of the bends in the individual fibers to return to their decreased angles, increasing their radial width of the fibers and decreasing their length, when an amount of radial compression is decreased, said implant being further configured to conform to the lumen of the hollow anatomical structure following insertion therein and to radially fill said hollow anatomical structure; and a tether secured to said distal section of said implant and extending along the entire length of said implant and substantially parallel thereto; said plurality of fibers being formed into an elongate bundle of fibers comprising at least about 500 fibers, said bundle being folded back along its longitudinal axis to form said implant, said implant having a folded end adjacent the distal section of the implant and a pair of elongate branches extending from said folded end of said implant, the elongate branches lying closely adjacent one another and extending parallel to one another along the length of said implant; said fibers of said elongate branches remaining loose wherein they are free to move and are not generally confined or restrained relative to each other. an implant sized for insertion into said hollow anatomical structure, said implant being elongate wherein said implant has an axial dimension which is greater than its radial dimension, said implant having a distal section and a proximal section; implant comprising a plurality of loose, non-knit and non-woven fibers, each fiber having a number of bends along the length thereof, each bend having an angle such that when each fiber is compressed radially, the bend angle generally increases and the fiber has a greater axial length and a smaller radial width than when uncompressed, each of said fibers being formed from one or more bioabsorbable materials and having a denier of about 0.1 to about 10; said implant being radially compressible to facilitate insertion into said hollow anatomical structure, and said implant being expandable toward a radially larger, less radially dense elongate configuration, the expansion facilitated by a tendency of the bends in the individual fibers to return to their decreased angles, increasing their radial width of the fibers and decreasing their length, when an amount of radial compression is decreased, said implant being further configured to conform to the lumen of the hollow anatomical structure following insertion therein and to radially fill said hollow anatomical structure; and a tether secured to said distal section of said implant and extending along the entire length of said implant and substantially parallel thereto; said plurality of fibers being formed into an elongate bundle of fibers comprising at least about 500 fibers, said bundle being folded back along its longitudinal axis to form said implant, said implant having a folded end adjacent the distal section of the implant and a pair of elongate branches extending from said folded end of said implant, the elongate branches lying closely adjacent one another and extending parallel to one another along the length of said implant; said fibers of said elongate branches remaining loose wherein they are free to move and are not generally confined or restrained relative to each other.