A trawl door (20, 60) or a paravane (120, 140) having at least one main deflector (22, 22U, 22L) includes a permeable structure disposed adjacent to and separated from an outer surface (34) of the main deflector (22, 22U, 22L). The permeable structure extends from near a trailing edge (26, 26U, 26L) of the main deflector (22, 22U, 22L) over and separated from the outer surface (34) toward the maindeflector's leading edge (24, 24U, 24L). In one embodiment of the permeable structure, a plurality of apertures (54, 56) pierce a perforated slat (52, 52U, 52L) thereby establishing a porous surfaceadjacent to the outer surface (34) of the main deflector (22, 22U, 22L). Adding the permeable structure perforated slat (52, 52U, 52L) to a trawl door (20, 60) increases the trawl door's stability when the trawl door is towed through water at a high angle of attack, and also reduces the trawl door's drag when operating at a high angle of attack.