  Clean materials are required to construct and operate many low-background
physics experiments. High-purity copper has found broad use because of its
physical properties and availability. In this paper, we describe methods to
assay and mitigate $^{210}$Pb contamination on copper surfaces, such as from
exposure to environmental radon or coming from bulk impurities. We evaluated
the efficacy of wet etching on commercial samples and observed that $^{210}$Po
contamination from the copper bulk does not readily pass into solution. During
the etch, the polonium appears to trap at the copper-etchant boundary, such
that it is effectively concentrated at the copper surface. We observed a
different behavior for $^{210}$Pb; high-sensitivity measurements of the alpha
emissivity versus time indicate the lowest level of $^{210}$Pb contamination
ever reported for a commercial copper surface: $0\pm12$ nBq/cm$^2$ (1$\sigma$).
Additionally, we have demonstrated the effectiveness of mitigating trace
$^{210}$Pb and $^{210}$Po surface backgrounds using custom, high-purity
electroplating techniques. These approaches were evaluated utilizing assays
performed with an XIA UltraLo-1800 alpha spectrometer.
