The Multi-Spectral Solar Telescope Array was launched from White Sands Missile Range, New Mexico, on 1991 May 13 at 1905 UT. Full-disk, high-resoluton solar images were obtained in a variety of soft X-ray and far-ultraviolet wavelengths. The 193 Angstrom (Fe XII) and 44 Angstrom (Si XII) images show a large number of coronal bright points. The high spatial resolution of the Fe XII image allows many of the bright points to be resolved as tiny loops. Co-alignment of the soft X-ray images with the 1216 Angstrom Ly alpha image reveals that all the coronal bright points have counterparts in the transition region, often resolved as a pair of footpoints, which are brighter than neighboring elements of the chromospheric network. Moreover, comparison with the KPNO magnetogram shows dipole structures coincident with nearly all of the bright points. We present a quantitative analysis based on preliminary photometry of four of the bright points that were observed. By fitting a simple, numerical loop model to the photometric data, we estimate the magnitude of the coronal heating in these structures. The rate of heating per unit footpoint area is found to be similar to previous measurements for much larger coronal structures. Implications for heating of the chromosphere and lower transition region are also discussed.