A surgical filament snare assembly including an anchor capable of being fixated in bone and having a filament engagement feature. A first filament has a noose with first and second noose limbs connected, preferably slidably connected, to the filament engagement feature of the anchor. The first and second noose limbs emerge from the anchor as first and second free filament limbs which are capable of being passed through tissue to be repaired and then passable through the noose. The noose, such as one or more half-hitches, is capable of receiving the free filament limbs and strangulating them when tension is applied to at least one of the free filament limbs and the noose to enable incremental tensioning of the tissue after the anchor is fixated. Preferably, the snare assembly further includes a flexible sleeve joining at least some portion of the first and second free filament limbs to facilitate passing of the free filament limbs at least through the tissue as a single unit.