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Collisionless shock acceleration of protons and C^{6+} ions has been achieved by the interaction of a 10^{20}  W/cm^{2}, 1  μm laser with a near-critical density plasma. Ablation of the initially solid density target by a secondary laser allows for systematic control of the plasma profile. This enables the production of beams with peaked spectra with energies of 10–18  MeV/amu and energy spreads of 10%–20% with up to 3×10^{9} particles within these narrow spectral features. The narrow energy spread and similar velocity of ion species with different charge-to-mass ratios are consistent with acceleration by the moving potential of a shock wave. Particle-in-cell simulations show shock accelerated beams of protons and C^{6+} ions with energy distributions consistent with the experiments. Simulations further indicate the plasma profile determines the trade-off between the beam charge and energy and that with additional target optimization narrow energy spread beams exceeding 100  MeV/amu can be produced using the same laser conditions.