We report on the selective acceleration of carbon ions during the interaction of ultrashort, circularly polarized and contrast-enhanced laser pulses, at a peak intensity of 5.5×10^{20} W/cm^{2}, with ultrathin carbon foils. Under optimized conditions, energies per nucleon of the bulk carbon ions reached significantly higher values than the energies of contaminant protons (33 MeV/nucleon vs 18 MeV), unlike what is typically observed in laser-foil acceleration experiments. Experimental data, and supporting simulations, emphasize different dominant acceleration mechanisms for the two ion species and highlight an (intensity dependent) optimum thickness for radiation pressure acceleration; it is suggested that the preceding laser energy reaching the target before the main pulse arrives plays a key role in a preferential acceleration of the heavier ion species.