Analysis of carbon emissions paths stabilizing atmospheric CO{sub 2} in the 350--750 ppmv range reveals that implementing the UN Climate Convention will become increasingly difficult as the stabilization target decreases because of increasing dependence on carbon-free energy sources. Even the central Intergovernmental Panel on Climate Change scenario (IS92a) requires carbon-free primary power by 2050 equal to the humankind`s present fossil-fuel-based primary power consumption {approximately}10 TW (1 TW = 10{sup 12} W). The authors describe and critique the assumptions on which this projection is based, and extend the analysis to scenarios in which atmospheric CO{sub 2} stabilizes. For continued economic growth with CO{sub 2} stabilization, new, cost-effective, carbon-free technologies that can provide primary power of order 10 TW will be needed in the coming decades, and certainly by mid-century, in addition to improved economic productivity of primary energy.