An annuloplasty structure includes a flexible sleeve and an elongate contraction wire. The sleeve has a first sleeve-end-portion, a second sleeve-end-portion, and a circumferential wall that defines a longitudinal lumen between the first and second sleeve-end-portions. The contraction wire has a first wire-end and a second wire-end, the first wire-end being attached to the sleeve at the first sleeve-end-portion. The wire extends, in association with the circumferential wall, from the first sleeve-end-portion to the second sleeve-end-portion. The wire is arranged with respect to the sleeve such that increasing a longitudinal proportion of the wire that is disposed within the lumen longitudinally contracts the sleeve. Other embodiments are also provided.
