A system for treating a tissue site includes a pressure source to apply reduced pressure, and a manifold in fluid communication with the pressure source to provide reduced pressure to the tissue site. The system includes a drape for adhering to the tissue site to cover the tissue site and the manifold. The drape has a film layer having a thickness less than about 15 microns, and an adhesive coupled to the film layer. The adhesive seals the film layer to the tissue site to create a sealed space having the manifold therein. The adhesive is sufficiently thick to limit leaks between the film layer and the tissue site.