A tubular, radially self-expanding stent includes a latticework of interbraided, helically wound resilient structural strands. An axial control member is secured to the tubular latticework at axially spaced apart proximal and distal coupling locations. At the proximal location, the control member is coupled slidably, to permit an adjustment of the axial distance between the coupling locations, thus to selectively adjust the radius profile of the latticework between the two locations. To set a desired radius profile, the control member either is crimped near the proximal location or fixed within a self-locking connector. The control members, preferably monofilament strands, can be elastic or substantially inextensible. Two or more control members can be used if desired. In an alternative embodiment, recovery metal control members are fixed at their opposite ends to the latticework, then plastically deformed by elongation to axially elongate and radially reduce the latticework. Following deployment, the control members are heated sufficiently to cause the control members to return to their shorter, nominal shapes, to axially shorten and radially enlarge the stent. Both versions preferably feature selvaged ends.