A study of LEED fine structure on the low-index planes of copper reveals that surface barrier resonances are present on all planes at low energies. The resonance features are strong on the (111) and (100) and weak on the (110) plane. Ordered oxygen chemisorption strengthens the resonances while disordered oxygen adsorption weakens them. A theoretical analysis shows that the saturated image barrier is an adequate barrier model for the resonance process. Trends in surface barrier structure between the different low-index planes of copper are discussed.