This study presents a novel design and techno-economic analysis of processes for the purification of captured CO2 from the flue gas of an oxy-combustion power plant fueled by petroleum coke. Four candidate process designs were analyzed in terms of GHG emissions, thermal efficiency, pipeline CO2 purity, CO2 capture rate, levelized costs of electricity, and cost of CO2 avoided. The candidates were a classic process with flue-gas water removal via condensation, flue-gas water removal via condensation followed by flue-gas oxygen removal through cryogenic distillation, flue-gas water removal followed by catalytic conversion of oxygen in the flue gas to water via reaction with hydrogen, and oxy-combustion in a slightly oxygen-deprived environment with flue-gas water removal and no need for flue gas oxygen removal. The former two were studied in prior works and the latter two concepts are new to this work. The eco-technoeconomic analysis results indicated trade-offs between the four options in terms of cost, efficiency, lifecycle greenhouse gas emissions, costs of CO2 avoided, technical readiness, and captured CO2 quality. The slightly oxygen-deprived process has the lowest costs of CO2 avoided, but requires tolerance of a small amount of H2, CO, and light hydrocarbons in the captured CO2 which may or may not be feasible depending on the CO2 end use. If infeasible, the catalytic de-oxygenation process is the next best choice. Overall, this work is the first study to perform eco-technoeconomic analyses of different techniques for O2 removal from CO2 captured from an oxy-combustion power plant.