A multi-component stent-graft system (10) comprises first, second, and third generally tubular stent-grafts (20, 22, 24), which are configured to assume radially-expanded states. The first (20) is shaped so as to define a first lateral opening (34) when radially-expanded. The second (22) is shaped so as to define a second lateral opening (44) when radially-expanded. The first and second (20, 22) are configured such that the second (22) forms a blood-impervious seal with the first (20) around the first lateral opening (34) when the second stent-graft (22) is disposed therethrough, and the first and the second (20, 22) are radially-expanded. The second and the third (22, 24) are configured such that the third (24) forms a blood-impervious seal with the second (22) around the second lateral opening (44) when the third (24) is disposed therethrough, and the second and third (22, 24) are radially-expanded. Other embodiments also described.