Several methods of pumping air to an annular cooling passage surrounding a typical axial-flow turbojet-engine afterburner were evaluated and compared on the basis of thrust and specific fuel consumption of the systems. Each system was analyzed over a range of afterburner-wall temperatures, flight Mach numbers, and exhaust-gas temperatures at sea level and 35,000 feet. Ram pressure recovery, boundary-layer pressure recovery, and the engine-jet actuated ejector appear to be satisfactory systems at high Mach numbers. Cooling with compressor-exit air bleed was found to be unsatisfactory,but the use of compressor-exit bleed air as the primary fluid in a high-performance ejector was satisfactory. The use of an auxiliary compressor driven from the engine shaft increased the thrust and decreased the specific fuel consumption of the engine for many of the conditions investigated.