Recently it has been postulated that a post combustion capture process with three membrane stages and cryogenic separation can achieve high CO2 recovery and purity while being economically competitive with existing commercial carbon capture technology (Merkel et al., 2010). The advantage of this design is the use of burner feed air as a membrane sweep gas to ensure high CO2 recovery. However, this results in dilution of oxygen in the burner and reduces the overall efficiency of the power station. In this study, two modifications to this process are considered. First, to ensure that the feed burner air supply is not oxygen deficient, we consider the addition of a small air separation membrane unit on this feed air supply. The O2 enrichment design allows much greater CO2 concentrations to be accommodated within this burner air supply. The resulting capture cost of the optimised process is reduced to less than US$ 32 per tonne avoided, with a burner air supply containing 33 mol% CO2. If flue gas desulphurisation and selective catalytic reduction are required then the cost of capture is less than US$ 43 per tonne avoided. However, one of the consequences of the oxygen enrichment is the need for four membrane stages which may limit its practical application. In comparison, a simplified process that removes the final CO2 membrane concentration while still achieving high CO2 recovery has increased energy demand and operating costs but results in lower overall capital cost. The cost of capture of this simplified process remains comparable at less than US$ 35 per tonne avoided for a sweep gas containing 9 mol% CO2.