A crimp sleeve, for connection of the back shell of a fiber optic cable connector with a fiber optic cable of a type including a buffered optic fiber having an encircling jacket inclusive of fibrous matter, includes a crimpable body member having first and second open ends and defining a passage between the first and second open ends, the crimpable member having first and second interior surfaces bounding the passage successively lengthwise of the body member. The first interior surface extends from the first open end interiorly of the body member and has a first radius relative to a central axis of the body member and the second interior surface has a second radius relative to the central axis of the body member of measure less than the first radius. The first interior surface is adapted, upon crimping of the body member onto the cable, to retentively engage exposed fibrous matter of the cable and the second interior surface is adapted, upon crimping of the body member onto the cable, to retentively engage the jacket of the cable adjacent the exposed fibrous matter.