The stability of the disordered glassy phase in the relaxors PbMg 1/3 Nb 2/3 O 3 and (PbMg 1/3 Nb 2/3 O 3) 0.88 (PbTiO 3) 0.12 , called PMN and PMN-PT, was investigated by preparing partially polarized samples and allowing them to age at zero field in the temperature range for which the phase is history-dependent. The PMN-PT polarization would spontaneously increase until long-range order formed, first appearing as giant polarization noise. Thus the thermodynamically stable phase in PMN-PT appears to be ferroelectric. In contrast, a PMN sample lacking the sharp first-order field-driven transition found in some other samples spontaneously depolarized, consistent with its glassy state being thermodynamically stable. Detailed thermal depolarization results in PMN show two distinct broad peaks as well as a small fraction of material with a distribution of abrupt melting transitions.