For cool roofs the combined effect of the three parameters that define heat gain and loss from a roof, namely solar albedo a, thermal emittance E, and sub-roof R-value, must be considered. An accurate contribution of night sky cooling, and hence humidity and total down-welling atmospheric radiation is needed. A systematic analysis of the contribution of a roof to average cooling load per day and to peak load reductions is presented for a temperate climate zone over 6 cooling months using an hour-by-hour analysis. Eighteen 3-parameter sets (a,E,R) demonstrate the over-riding importance of a high a, while sensitivity to R-value and E drops away as albedo rises. Up-front cost per unit reductions in peak demand or average energy use per day always rises strongly as R rises unless albedo is low. A moderate R similar to 1.63 is superior to high R unless a roof is dark, or winter heating demand is high. We indicate briefly why the roof typically does not present a dominant influence on average winter heating needs in most temperate zones, enhancing the benefits of cool roofs. (C) 2011 Elsevier B.V. All rights reserved.