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The shape of metal nanoparticles can dramatically depend on reaction conditions. While Pt nanoparticles are known to dynamically respond to the partial pressure of CO, in situ TEM images show that, surprisingly, Co nanoparticles do not change their shape under a CO atmosphere despite going through several reconstructions. Detailed DFT calculations attribute this contrasting behavior to two factors: (1) CO adsorption has a higher stabilization effect on the high-index facets of Pt than on those of Co; (2) the Co surface energy is more sensitive to the coordination number, making high-index surfaces less stable relative to Pt. These two factors combined can affect the stability of high-index surfaces as is the case for Pt nanoparticles, which reconstruct already at low CO pressures. In the case of Co nanoparticles, the low-index surface remains the most stable even at high CO partial pressures. The robustness of the shape of Co nanoparticles challenges recent proposals that high-index facets, which facilitate direct CO dissociation, are present on Co nanoparticle catalysts under Fischer–Tropsch conditions.