It is well known that at the gel-liquid phase-transition temperature a lipid bilayer membrane exhibits an increased ion permeability. We analyze the quantized currents in which the increased permeability presents itself. The open time histogram shows a "-3/2" power law which implies an open-closed transition rate that decreases like k(t)∝t(-1) as time evolves. We propose a "pore freezing" model to explain the observations. We discuss how this model also leads to the 1/fα noise that is commonly observed in currents across biological and artificial membranes.