The present invention relates to an external cooling system for a molten film tube produced by a blown film tubular extrusion process, comprised of one or more enclosures with one or more respective cavities that directly receive a portion of cooling gas emanating from one or more associated cooling elements. Each enclosure includes a port containing a variable exhaust device and optional flow buffer, acting to maintain a pressure differential between the cavity and an adjacent inside volume of the molten film tube, adjustable to optimize molten film tube stability cooling element efficiency and spaced apart dimension between cooling elements. Significant increases in production speeds are achieved with improved film quality over an increased range of tubular film sizes, down to a minimum size which occurs when operating at zero internal to molten film tube pressure.