Activated carbons prepared from petroleum pitch and using KOH as activating agent exhibit an excellent behavior in CO2 capture both at atmospheric (∼168 mg CO2/g at 298 K) and high pressure (∼1500 mg CO2/g at 298 K and 4.5 MPa). However, an exhaustive evaluation of the adsorption process shows that the optimum carbon structure, in terms of adsorption capacity, depends on the final application. Whereas narrow micropores (pores below 0.6 nm) govern the sorption behavior at 0.1 MPa, large micropores/small mesopores (pores below 2.0–3.0 nm) govern the sorption behavior at high pressure (4.5 MPa). Consequently, an optimum sorbent exhibiting a high working capacity for high pressure applications, e.g., pressure-swing adsorption units, will require a poorly-developed narrow microporous structure together with a highly-developed wide microporous and small mesoporous network. The appropriate design of the preparation conditions gives rise to carbon materials with an extremely high delivery capacity ∼1388 mg CO2/g between 4.5 MPa and 0.1 MPa. Consequently, this study provides guidelines for the design of carbon materials with an improved ability to remove carbon dioxide from the environment at atmospheric and high pressure.