A tubular prosthesis that includes a scaffolding formed by at least one scaffolding filament; a cover; and at least one controlled ingrowth feature constructed and arranged to abut an inner surface of a lumen wall when the prosthesis is implanted in the body lumen. The controlled ingrowth feature may extend inwards or outwards from the prosthesis outer surface. The controlled ingrowth feature may be formed by a scaffolding filament; by a separate filament; by the cover; and combinations thereof.