We present bremsstrahlung-isochromat-spectroscopy and synchrotron-radiation photoemission-spectroscopy studies of CdTe single crystals cleaved in situ. The photoemission data, and empirical-pseudopotential calculations of the band structure, were used to reevaluate the position of valence and core spectral features. The bremsstrahlung-isochromat-spectroscopy results emphasize structure in the conduction-band density of states at 4.1, 6.7, 9.6, 11.3, 12.5, and 15 eV above the valence-band maximum. The calculations are found to reproduce the conduction-band structure throughout a range of 18 eV above the valence-band maximum.