Copper electrodes have been shown to be selective toward the electroreduction of carbon dioxide to ethylene, carbon monoxide, or formate. However, the underlying causes of their activities, which have been attributed to a rise in local pH near the surface of the electrode, presence of atomic-scale defects, and/or residual oxygen atoms in the catalysts, etc., have not been generally agreed on. Here, we perform a study of carbon dioxide reduction on four copper catalysts from -0.45 to -1.30 V vs. reversible hydrogen electrode. The selectivities exhibited by 20 previously reported copper catalysts are also analyzed. We demonstrate that the selectivity of carbon dioxide reduction is greatly affected by the applied potentials and currents, regardless of the starting condition of copper catalysts. This study shows that optimization of the current densities at the appropriate potential windows is critical for designing highly selective copper catalysts.