An endovascular prosthesis includes a stent-graft and an external coagulation inducer. The stent-graft includes a first portion of structural strut members and a first portion of a graft member, which, when the endovascular prosthesis is unconstrained in a radially-expanded state, together are shaped so as to define a blood-carrying tubular structure defining a lumen. The external coagulation inducer includes an extra-luminal skirt, which includes a second portion of the structural strut members and a second portion of the graft member, and is configured to assume: (i) when the endovascular prosthesis is removably disposed in a delivery sheath, a radially-compressed delivery state, in which the structural strut members of the first portion do not coincide with the structural stent members of the second portion, and (ii) when the endovascular prosthesis is unconstrained, a radially-expanded state, in which the extra-luminal skirt extends radially outward from an external surface of the stent-graft.