Described embodiments include apparatus (28) that includes a shunt (26). The shunt includes a flared distal portion (40), a flared proximal portion (44), and an intermediate portion (42), disposed between the distal portion and the proximal portion. The apparatus further includes a constricting flexible longitudinal element (38) passing circumferentially along the intermediate portion of the shunt, configured to constrict the intermediate portion of the shunt, and one or more proximal-portion-collapsing flexible longitudinal elements (36) configured to collapse the proximal portion of the shunt. Other embodiments are also described.