We present an analysis of solar coronal emission lines formed above 2.5 MK observed with the Extreme-Ultraviolet Imaging Spectrometer on Hinode during a small flare. Our main purpose is to evaluate the internal consistency of the atomic data available for the observed emission. We find that the observed emission from high-temperature Ca lines (Ca XIV, XV, XVI, and XVII) is generally consistent with the available atomic data. The observed Fe XVII emission at these wavelengths, in contrast, is more difficult to reconcile with current atomic calculations. The energy levels tabulated in the CHIANTI atomic physics database generally do not correspond to the observed wavelengths. After associating the calculated emissivities with the observed emission by hand, we find that the observed intensities are roughly consistent with what is predicted. However, the intensity of the strongest unblended line, Fe XVII 254.87 A, is not consistent with the intensities of the other Fe XVII lines at these wavelengths. Several of the Ca XV emission lines, which are formed at about 4 MK, form density-sensitive line ratios in the range log ne = 9–11 cm−3. Density measurements at these temperatures are potentially important for understanding the coronal heating mechanism. Our initial analysis suggests that high-temperature active region plasma is underdense relative to the predictions of steady heating models.