X-ray bright points are small, million-degree features in the solar atmosphere composed of short coronal loops. They are magnetically driven structures associated with photospheric magnetic bipoles. Their relatively small size and simple structure suggest they are ideal candidates for comparisons with coronal heating models. In this paper, we present the analysis of 12 bright points using data from the EUV Imaging Spectrometer on Hinode and the Michelson Doppler Imager on Solar and Heliospheric Observatory. Using the spectroscopy data, we construct differential emission measure (DEM) curves, calculate the electron density, and find DEM-weighted temperatures. In addition, we determine the most likely ionization balance. Using the magnetic field observations, we complete potential field extrapolations of the magnetograms and estimate the loop lengths. Using this information, we construct models assuming the bright points are formed of hundreds of strands, each heated steadily and uniformly. We formulate the models so that the observed emission measure distribution is matched within a few percent. We then compare the densities determined from the models, (1.4-5.0) × 109, to those calculated from spectral data, (0.6-2.0) × 109. We find the majority of bright points do not agree with steady uniform heating models; instead they are underdense relative to their expected density by a factor of 0.16-0.82.