Large-amplitude, low-frequency electric fields can be used to burn spectral holes in the dielectric response of supercooled propylene carbonate and glycerol. This ability to selectively modify the dielectric response establishes that the non-Debye behavior results from a distribution of relaxation times, Refilling of the spectral hole was consistent with a single recovery time that coincided with the peak in the distribution. Moreover, refilling occurred without significant broadening, which indicates negligible direct exchange between the degrees of freedom that responded to the field. Nonresonant spectral hole burning facilitates direct investigation of the intrinsic response of systems that exhibit nonexponential relaxation.