Apparatus comprising a generally tubular endovascular self-curving stent-graft (20), which (a) comprises a self-curving longitudinal portion (22) having proximal and distal ends (23, 25), (b) is configured to transition from a radially-compressed delivery state to a radially-expanded state, wherein, when the stent-graft (20) is unconstrained in the radially-expanded state, the self-curving longitudinal portion (22) of the stent-graft (20) is curved so as to define an innermost curve (26) and an outermost curve (28), and (c) comprises: a plurality of circumferential strut members (30), disposed at respective axial positions along the self-curving longitudinal portion (22) of the stent-graft (20), surrounding a central longitudinal axis (36) of the self-curving longitudinal portion (22) of the stent-graft (20), wherein each of the circumferential strut members (30) of the self-curving longitudinal portion (22) is shaped so as to define a plurality of proximal peaks (66)； and a graft member (32), which comprises one or more substantially blood-impervious flexible sheets (34), and which is fixed to the circumferential strut members (30), wherein, when the stent-graft (20) is unconstrained in the radially-expanded state, for at least one of the circumferential strut members (30) of the self-curving longitudinal portion (22): a first set (68A) of the proximal peaks (66) of the circumferential strut member (30), which includes at least a circumferentially-closest one of the proximal peaks (66) to the outermost curve (28) of the self-curving longitudinal portion (22), and no more than half of the proximal peaks (66) of the circumferential strut member (30), are bent radially inward at least an average angle of 20 degrees toward the central longitudinal axis (36) of the self-curving longitudinal portion (22), and a second set (68B) of the proximal peaks (66) of the circumferential strut member (30), which includes all of the proximal peaks (66) of the circumferential strut m
