Apparatus and a method for the provision of TNP therapy to a wound are described, the apparatus comprising: a sealing membrane (504) for covering a wound to form a wound cavity (500); one end of an aspirant conduit (522) operably associated with the wound cavity, vacuum means (524) provided at a distal end of the aspirant conduit for applying a vacuum to the wound cavity; and, air bleed means (510) in fluid communication with the wound cavity. Various embodiments of air bleed port members are also described.