Apparatus comprising a generally tubular stent-graft, which has distal and proximal stent-graft ends (36, 38) and comprises: a generally tubular support element, which comprises a plurality of structural stent elements; and a covering element that is attached to and at least partially covers the support element, wherein when the stent-graft is unconstrained in a radially-expanded state: the covering element and the support element are shaped so as to together define a lateral fenestration having distal and proximal fenestration ends (35, 37), a first perimeter of the distal stent-graft end equals at least 200% of a second perimeter of the proximal stent-graft end, and the stent-graft includes a dissection-reinforcement axial portion, which (a) includes a portion of the structural stent elements, (b) has (i) a distal dissection-reinforcement end and (ii) a proximal dissection-reinforcement end that is disposed along the stent-graft no more than 20 mm proximal to the proximal fenestration end, (c) has an axial length along the stent-graft that is equal to between 5% and 32% of a greatest perimeter of the stent-graft between the distal fenestration end and the distal stent-graft end, and (d) has a radial strength that is at least 10% greater than an average radial strength of the entire stent-graft. a generally tubular support element, which comprises a plurality of structural stent elements; and a covering element that is attached to and at least partially covers the support element, wherein when the stent-graft is unconstrained in a radially-expanded state: the covering element and the support element are shaped so as to together define a lateral fenestration having distal and proximal fenestration ends (35, 37), a first perimeter of the distal stent-graft end equals at least 200% of a second perimeter of the proximal stent-graft end, and the stent-graft includes a dissection-reinforcement axial portion, which (a) includes a portion of the structural stent elements, (b) has (i) a distal dissection-reinforcement end and (ii) a proximal dissection-reinforcement end that is disposed along the stent-graft no more than 20 mm proximal to the proximal fenestration end, (c) has an axial length along the stent-graft that is equal to between 5% and 32% of a greatest perimeter of the stent-graft between the distal fenestration end and the distal stent-graft end, and (d) has a radial strength that is at least 10% greater than an average radial strength of the entire stent-graft. the covering element and the support element are shaped so as to together define a lateral fenestration having distal and proximal fenestration ends (35, 37), a first perimeter of the distal stent-graft end equals at least 200% of a second perimeter of the proximal stent-graft end, and the stent-graft includes a dissection-reinforcement axial portion, which (a) includes a portion of the structural stent elements, (b) has (i) a distal dissection-reinforcement end and (ii) a proximal dissection-reinforcement end that is disposed along the stent-graft no more than 20 mm proximal to the proximal fenestration end, (c) has an axial length along the stent-graft that is equal to between 5% and 32% of a greatest perimeter of the stent-graft between the distal fenestration end and the distal stent-graft end, and (d) has a radial strength that is at least 10% greater than an average radial strength of the entire stent-graft.