At last, all the major emitters of greenhouse gases (GHGs) have agreed under the Copenhagen Accord that global average temperature increase should be kept below 2 degrees C. This study develops the criteria for limiting the warming below 2 degrees C, identifies the constraints imposed on policy makers, and explores available mitigation avenues. One important criterion is that the radiant energy added by human activities should not exceed 2.5 (range: 1.7-4) watts per square meter (Wm(-2)) of the Earth's surface. The blanket of man-made GHGs has already added 3 (range: 2.6-3.5) Wm(-2). Even if GHG emissions peak in 2015, the radiant energy barrier will be exceeded by 100%, requiring simultaneous pursuit of three avenues: (i) reduce the rate of thickening of the blanket by stabilizing CO(2) concentration below 441 ppm during this century (a massive decarbonization of the energy sector is necessary to accomplish this Herculean task), (ii) ensure that air pollution laws that reduce the masking effect of cooling aerosols be made radiant energy-neutral by reductions in black carbon and ozone, and (iii) thin the blanket by reducing emissions of short-lived GHGs. Methane and hydrofluorocarbons emerge as the prime targets. These actions, even if we are restricted to available technologies for avenues ii and iii, can reduce the probability of exceeding the 2 degrees C barrier before 2050 to less than 10%, and before 2100 to less than 50%. With such actions, the four decades we have until 2050 should be exploited to develop and scale-up revolutionary technologies to restrict the warming to less than 1.5 degrees C.