Slow polarization relaxation of a ferroelectric in a weak electric field is investigated in triglycine sulfate crystals with different states of the domain structure and surface. An automated setup is described that allows one to register relaxation with record accuracy. It is shown that under conditions of little change in the “degree of metastability” of the structure, the variation of the polarization ΔP with time t follows the law ΔP=C/(1+t/ta)n in all cases, where the parameters C, a, and n depend on the state of the structure and the surface. We present a phenomenological analysis of the experimental data based on the assumption that the nuclei are independent and contribute additively to the total polarization of the crystal, and construct spectra of the energy barriers of the domain walls. Aspects of the transformation of the spectra with variation of the nature of the domain structure, depth of surface relief, and magnitude of the external electric field are elucidated.