The present embodiments provide an endoluminal prosthesis, comprising a prosthetic trunk and a prosthetic branch, each comprising proximal and distal ends and a lumen extending therebetween. The proximal end of the prosthetic branch is secured around an aperture formed in a side surface of the prosthetic trunk. A support structure is coupled to the prosthetic branch. In certain embodiments, a proximal end of the support structure comprises a first width, and a distal end of the support structure comprises a second width, wherein the first width is less than the second width.