Methods for producing high purity fused silica (HPFS) glass having desired levels of dissolved hydrogen are provided. The methods involve measuring the level of hydrogen in the cavity of the furnace used to produce the glass and controlling the pressure within the furnace and/or gas flows to the furnace's burners so that the measured concentration has a desired value. In this way, the level of dissolved hydrogen in the glass can be controlled since, as shown in FIG. 3, there is a direct correlation between the hydrogen concentration in the cavity atmosphere and level of dissolved hydrogen in the glass.