An apparatus for treating a hollow anatomical structure, said apparatus comprising: an implant sized for insertion into said hollow anatomical structure through an access site, said implant having a distal section and a proximal section; said implant being radially compressible to facilitate insertion into said hollow anatomical structure, and said implant being self-expandable toward a radially larger, less dense elongate configuration, in which said implant is configured to conform longitudinally to the lumen of the hollow anatomical structure following insertion therein and to fill said hollow anatomical structure such that an outer circumferential surface of said implant substantially engates an inner surface of said hollow anatomical structure, the implant having a cross-sectional width of 12-60 French when the implant is in an expanded state, and having an axial length between 1 cm and 60 cm; said implant comprising a plurality of loose, non-knit and nonwoven fibers, each figer being bulked in a radial direction and being formed from one or more bioabsorbable materials, each of said fibers being 0.1 to 10 denier; said plurality of fibers being formed into an elongate bundle of fibers comprising between 500 and 500,000 fibers, said bundle being folded back along its longitudinal axis to form said implant, said implant havig a folded end forming 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; said elongate branches remaining loose wherein they are free to move and are not confined or restrained relative to each other except at said folded end; and a tether having a distal end and a proximal end, the distal end secured to said distal section of said implant and the proximal end configured to be secured near the access site. an implant sized for insertion into said hollow anatomical structure through an access site, said implant having a distal section and a proximal section; said implant being radially compressible to facilitate insertion into said hollow anatomical structure, and said implant being self-expandable toward a radially larger, less dense elongate configuration, in which said implant is configured to conform longitudinally to the lumen of the hollow anatomical structure following insertion therein and to fill said hollow anatomical structure such that an outer circumferential surface of said implant substantially engates an inner surface of said hollow anatomical structure, the implant having a cross-sectional width of 12-60 French when the implant is in an expanded state, and having an axial length between 1 cm and 60 cm; said implant comprising a plurality of loose, non-knit and nonwoven fibers, each figer being bulked in a radial direction and being formed from one or more bioabsorbable materials, each of said fibers being 0.1 to 10 denier; said plurality of fibers being formed into an elongate bundle of fibers comprising between 500 and 500,000 fibers, said bundle being folded back along its longitudinal axis to form said implant, said implant havig a folded end forming 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; said elongate branches remaining loose wherein they are free to move and are not confined or restrained relative to each other except at said folded end; and a tether having a distal end and a proximal end, the distal end secured to said distal section of said implant and the proximal end configured to be secured near the access site.