Apparatus comprising a generally tubular endovascular self-curving stent-graft, 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; a graft member, which comprises one or more substantially blood-impervious flexible sheets, and which is fixed to the circumferential strut members; a compression-generation spring, which (a) is in an elongated configuration when the stent-graft is in the radially-compressed state, and (b) overlaps respective first portions of at least two of the circumferential strut members; and an anti-buckling spring, which (a) overlaps respective second portions of at least two of the circumferential strut members, (b) is shaped so as to define a plurality of curves, and (c) is in fixed orientation with respect to the graft member such that the curves reside substantially in a plane that is substantially parallel to the surface of the graft member, wherein the anti-buckling spring and the compression-generation spring are together configured to curve the self-curving longitudinal portion of the stent-graft when the stent-graft is unconstrained in the radially-expanded state, such that a lesser length of the self-curving longitudinal portion of the stent-graft, measured along the innermost curve, is less than 80% of a greater length of the self-curving longitudinal portion of the stent-graft, measured along the outermost curve. 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; a graft member, which comprises one or more substantially blood-impervious flexible sheets, and which is fixed to the circumferential strut members; a compression-generation spring, which (a) is in an elongated configuration when the stent-graft is in the radially-compressed state, and (b) overlaps respective first portions of at least two of the circumferential strut members; and an anti-buckling spring, which (a) overlaps respective second portions of at least two of the circumferential strut members, (b) is shaped so as to define a plurality of curves, and (c) is in fixed orientation with respect to the graft member such that the curves reside substantially in a plane that is substantially parallel to the surface of the graft member, wherein the anti-buckling spring and the compression-generation spring are together configured to curve the self-curving longitudinal portion of the stent-graft when the stent-graft is unconstrained in the radially-expanded state, such that a lesser length of the self-curving longitudinal portion of the stent-graft, measured along the innermost curve, is less than 80% of a greater length of the self-curving longitudinal portion of the stent-graft, measured along the outermost curve.