The Z Gaussian interference channel with weak interference is known to have at least two critical points in its capacity region. These are corner points where the slope of the region typically shows a sudden change. They occur at the points of unconditional maximum rate for one of the users and the maximum rate that can be accommodated by the other user. One of the corner points is well established. For the second corner point there are yet non-coinciding lower and upper bounds. In this talk we discuss an additional critical point in the achievable region of this channel, that comes about in the transition between the so called multiplex and overflow regions of the noiseberg encoding scheme.