Apparatus comprising a generally tubular endovascular self-curving stent-graft for implantation in a blood vessel, which (a) comprises a self-curving longitudinal portion 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 is unconstrained in the radially-expanded state, the self-curving longitudinal portion of the stent-graft is curved so as to define an innermost curve and an outermost curve, and (c) comprises: a plurality of circumferential strut members, disposed at respective axial positions along the self-curving longitudinal portion of the stent-graft, surrounding a central longitudinal axis of the self-curving longitudinal portion of the stent-graft, wherein each of the circumferential strut members of the self-curving longitudinal portion is shaped so as to define a plurality of proximal peaks; and a graft member, which comprises one or more substantially blood-impervious flexible sheets, and which is fixed to the circumferential strut members, characterized in that, when the stent-graft is unconstrained in the radially-expanded state, for at least one of the circumferential strut members of the self-curving longitudinal portion: a first set of the proximal peaks of the circumferential strut member, which includes at least a circumferentially-closest one of the proximal peaks to the outermost curve of the self-curving longitudinal portion, and no more than half of the proximal peaks of the circumferential strut member, are bent radially inward at least an average angle of 20 degrees toward the central longitudinal axis of the self-curving longitudinal portion, such inward bending of the first set of the proximal peaks being configured to avoid possible puncturing of the graft member and/or a wall of the blood vessel by the proximal peaks when the self-curving stent-graft is in the radially-expanded state; and a second set of the proximal peaks of the circumferential strut member, which includes all of the proximal peaks of the circumferential strut member not in the first set, are not bent radially inward by at least an average angle of 20 degrees toward the central longitudinal axis of the self-curving longitudinal portion. a plurality of circumferential strut members, disposed at respective axial positions along the self-curving longitudinal portion of the stent-graft, surrounding a central longitudinal axis of the self-curving longitudinal portion of the stent-graft, wherein each of the circumferential strut members of the self-curving longitudinal portion is shaped so as to define a plurality of proximal peaks; and a graft member, which comprises one or more substantially blood-impervious flexible sheets, and which is fixed to the circumferential strut members, characterized in that, when the stent-graft is unconstrained in the radially-expanded state, for at least one of the circumferential strut members of the self-curving longitudinal portion: a first set of the proximal peaks of the circumferential strut member, which includes at least a circumferentially-closest one of the proximal peaks to the outermost curve of the self-curving longitudinal portion, and no more than half of the proximal peaks of the circumferential strut member, are bent radially inward at least an average angle of 20 degrees toward the central longitudinal axis of the self-curving longitudinal portion, such inward bending of the first set of the proximal peaks being configured to avoid possible puncturing of the graft member and/or a wall of the blood vessel by the proximal peaks when the self-curving stent-graft is in the radially-expanded state; and a second set of the proximal peaks of the circumferential strut member, which includes all of the proximal peaks of the circumferential strut member not in the first set, are not bent radially inward by at least an average angle of 20 degrees toward the central longitudinal axis of the self-curving longitudinal portion. a first set of the proximal peaks of the circumferential strut member, which includes at least a circumferentially-closest one of the proximal peaks to the outermost curve of the self-curving longitudinal portion, and no more than half of the proximal peaks of the circumferential strut member, are bent radially inward at least an average angle of 20 degrees toward the central longitudinal axis of the self-curving longitudinal portion, such inward bending of the first set of the proximal peaks being configured to avoid possible puncturing of the graft member and/or a wall of the blood vessel by the proximal peaks when the self-curving stent-graft is in the radially-expanded state; and a second set of the proximal peaks of the circumferential strut member, which includes all of the proximal peaks of the circumferential strut member not in the first set, are not bent radially inward by at least an average angle of 20 degrees toward the central longitudinal axis of the self-curving longitudinal portion.