A dynamic fixation medical implant having at leasttwo bone anchors includes a longitudinal connectingmember assembly having rigid sleeves for attachment tothe bone anchors, at least one spacer engaging the boneanchors and the sleeves, and in some embodiments, an endelastic bumper. A flexible cord is initially slidinglyreceived within the rigid sleeves, the spacer and thebumper. The spacer may include an optional inelasticinner liner, with at least one of the sleeves having anextension slidingly receivable within the liner. Somesleeves include apertures for receiving a closure topportion for locking the cord against the sleeve, oralternatively receiving a closure top that does notextend into the aperture, the slip or grip optionprovided by the aperture in each sleeve resulting in anoverall connector with variable segmental stiffness.