We present new abundances derived from CuI, CuII, ZnI, and ZnII lines in six warm (5766<=T_eff_<=6427K), metal-poor (-2.50<=[Fe/H]<=-0.95) dwarf and subgiant (3.64<=logg<=4.44) stars. These abundances are derived from archival high-resolution ultraviolet spectra from the Space Telescope Imaging Spectrograph on board the Hubble Space Telescope and ground-based optical spectra from several observatories. Ionized Cu and Zn are the majority species, and abundances derived from CuII and ZnII lines should be largely insensitive to departures from local thermodynamic equilibrium (LTE). We find good agreement between the [Zn/H] ratios derived separately from ZnI and ZnII lines, suggesting that departures from LTE are, at most, minimal (<~0.1dex). We find that the [Cu/H] ratios derived from CuII lines are 0.36+/-0.06dex larger than those derived from CuI lines in the most metal-poor stars ([Fe/H]{<}-1.8), suggesting that LTE underestimates the Cu abundance derived from CuI lines. The deviations decrease in more metal-rich stars. Our results validate previous theoretical non-LTE calculations for both Cu and Zn, supporting earlier conclusions that the enhancement of [Zn/Fe] in metal-poor stars is legitimate, and the deficiency of [Cu/Fe] in metal-poor stars may not be as large as previously thought.