The present invention involves a draft stabilizing device mounted at the exit end of a draft vent or stack. The device is constructed from first and second cap members made in the form of open-bottomed cones which are substantially broader at their bases than they are high. The cones are joined together at their edges with their axes aligned. The lower cone has a large stack inlet opening at its apex which is connected to a stack. The lower cone also includes a plurality of outlet openings around its periphery. The area of the outlet openings exceeds the cross-sectional area of the stack.