Tape constructs for fixation of soft tissue to bone, or of soft tissue to soft tissue. The tape construct includes a thin tape material with at least one thread positioned on the exterior of the thin tape material. Preferably, two threads are provided only on the exterior of the thin tape material, the threads extending in a direction about longitudinal with the thin tape material and abutting the edges or rims of the tape. The two exterior threads act like a parachute for compression of tissue and also allow the tape to fold easily to reduce the diameter of the tape construct for tissue passing and instrument passing. The construct is a simple, collapsible, flexible, parachute-like structure that allows easy threading and passing through instruments.
