A low-pressure carbon filter process can capture carbon dioxide from combustion flue gas. This filter is filled with a carbonaceous sorbent, such as activated carbon, which has a high chemical affinity to and hence high capacity to retain CO2 but not nitrogen. This in turn leads to a high CO2/N-2 selectivity, especially at low pressures. While CO2 sorption is spontaneous and rapid, its recovery from the sorbent is a challenge that determines the process efficiency. Among the desorption methods considered in this work, direct steam can produce nearly pure CO2, but it results in condensed water in the bed that reduces the sorbent capacity and requires sorbent cooling, which is slow. Vacuum desorption in the absence of water also works, but it requires low pressures, much lower than 30 Torr, to achieve substantial CO2 yields. However, a hybrid approach, referred to as "steam-aided vacuum swing adsorption" (SA-VSA), proposed in this work, is found to alleviate or eliminate these problems. Water vapor serves as a displacement medium and hence increases the vacuum efficiency at moderate pressures. Vacuum, on the other hand, prevents bulk water condensation and sorbent heating, and hence eliminates the need for cooling. As a result, SA-VSA can completely recover nearly pure CO2 from combustion flue gas, but it also allows for optimizing the CO2 recovery and purity.