A generally tubular stent-graft (24) has distal and proximal stent-graft ends (36, 38) and includes a generally tubular support element (30) and a covering element (32). When the stent-graft (24) is unconstrained in a radially-expanded state: (1) the covering and support elements (32, 30) are shaped so as to together define a lateral fenestration (34) having distal and proximal fenestration ends (35, 37), (2) a perimeter (P1) of the distal stent-graft end (36) equals at least 200% of a perimeter (P2) of the proximal stent-graft end (38), and (3) the stent-graft (24) includes a dissection-reinforcement axial portion (48), which (a) has a proximal dissection-reinforcement end (52) that is disposed no more than 20 mm proximal to the proximal fenestration end (37), (b) extends along the stent-graft for a distance equal to between 5% and 32% of a greatest perimeter of the stent-graft (24) distally to the distal fenestration end (35), and (c) has a radial strength that is at least 10% greater than an average radial strength of the entire stent-graft (24). Other embodiments are also described.