A surgical system includes an insertion assembly and a drape shroud assembly mounted on the insertion assembly. When a sleeve of a surgical drape draping the insertion assembly is fastened to the drape shroud assembly, the sleeve is divided into two pockets. Instead of managing one long tube, the management problem of the drape sleeve is reduced to managing a plurality of shorter tubes. Shorter tubes make it easier for excess sleeve material to accordion as the tube length shortens instead of possibly bowing out and contacting a part of the insertion assembly or some other part of the surgical system.