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We report an Er-doped superfluorescent fiber source (SFS) with a record mean-wavelength stability of ±0.5 ppm over 17 h. This breakthrough was achieved in a double-pass SFS by implementing several improvements, namely 1) controlling all the parameters that affect its mean wavelength, including the pump diode temperature and current, 2) reducing polarization-induced drifts in mean wavelength with a Faraday rotator mirror and a long Er-doped fiber (EDF), and 3) getting rid of polarization controllers to eliminate polarization-dependent loss. The long-term mean-wavelength variations of this SFS were due almost entirely to variations in the EDF temperature. When the SFS temperature was allowed to vary, by calibrating its mean-wavelength dependence on temperature, it was possible to predict the mean wavelength to a ±2-ppm precision by simply measuring the EDF temperature. The same configuration was also implemented with a different Er-doped fiber to achieve an even lower dependence on EDF temperature. When controlling the temperature of this second SFS to about ±0.5°C, it exhibited a stability of ±0.5 ppm over 17 h. These new developments constitute an important step toward a practical high-grade fiber-optic gyroscope.