Pristine glass fiber is well known to become mechanically weaker when heat-treated in the presence of water vapor. However, recently, the same fiber was found to become stronger if heat-treated while held under a subcritical tensile stress at a temperature below the glass transition temperature. The added strength was attributed to the formation of a surface compressive layer on the glass created by a surface stress relaxation process that occurred while being held under the tensile stress in air. Silica glass fibers with strengths estimated to be~7-8 GPa were produced, exceeding the~5.5 GPa strength of fresh optical fiber commonly reported at room temperature in air. Similar degrees of strengthening, a 20-30% improvement, have been observed previously for E-glass and is reported here for the first time for soda-lime silicate glasses. This process is a new glass strenthening method that may be applied to all oxide glasses and is not subject to the same constraints as currently available methods.