A generally tubular stent-graft (20) includes a generally tubular support element (30) and a covering element (32) that is attached to and at least partially covers the support element (30). When the stent-graft (20) is unconstrained in a radially-expanded state, a proximal end portion (40) of the covering element (32) is shaped so as to define at least first and second proximally-extending pieces (42A, 42B). When the stent-graft (20) is unconstrained in the radially-expanded state and the proximally-extending pieces (42A, 42B) are fully proximally extended, the proximally-extending pieces (42A, 42B) (a) are shaped so as to define respective distal bases (46), which (i) have respective base lengths (L1) measured circumferentially around the stent-graft (20), and (ii) circumferentially circumscribe respective base arcs (a) of between 100 and 140 degrees, (b) are shaped so as to define respective proximal-most portions (48) more proximal than all other respective portions of the covering element (32) that circumscribe the respective base arcs (a), and (c) have respective axial lengths (L2) that equal between 50% and 150% of the respective base lengths (L1).
