Epitaxial copper layers, 20 nm to 1.5-m-thick, were grown on MgO͑001͒ by ultrahigh vacuum magnetron sputter deposition at 80°C. In situ electrical resistivity measurements indicate partial specular scattering at the Cu vacuum interface with a Fuchs-Sondheimer scattering parameter p = 0.6Ϯ 0.1. In situ deposition of 0.3 to 7.0-nm-thick Ta cap layers on the Cu surfaces leads to a resistivity increase, which is independent of the Ta thickness and is associated with a transition to completely diffuse surface scattering with p = 0.0Ϯ 0.1. The diffuse scattering is attributed to a "rough" electron potential at the Cu-Ta interface as well as to scattering into localized interface and surface states.