An endovascular stent-graft (10) includes a generally tubular hourglass-shaped body (22), which is configured to assume a radially-compressed delivery configuration and a radially-expanded deployment configuration. The hourglass-shaped body (22) includes a flexible stent member (26), which includes a plurality of structural stent elements (28) and a tubular fluid flow guide (24), which includes a fabric (29), and is attached to the structural stent elements (28). The hourglass-shaped body (22) is shaped so as to define a narrow waist portion (32) longitudinally surrounded by and adjacent to wider first and second longitudinal portions (30, 34). The fabric (29) along the waist portion (32) is shaped so as to define at least first and second lateral apertures (36, 38). Other embodiments are also described.