A high transmittance fairly clear/neutral colored glass composition is provided. An oxidizing agent(s) such as cerium oxide (e.g., CeO.sub.2) or the like is added to the glass batch in order to realize very oxidized conditions (i.e., to significantly lower the redox of the resulting glass). As a result of the oxidizing agent(s) used in the batch, the iron is oxidized to a very low FeO (ferrous state) content. For example, this may result in a glass having a glass redox value of no greater than 0.12 (more preferably <=0.10; even more preferably <=0.08; and most preferably <=0.05) and a % FeO (i.e., ferrous content) of from 0.0001 to 0.05%. In certain example embodiments, in order to compensate for yellow or yellow-green coloration a small amount of cobalt (Co) may be provided in the glass to enable it to realize a more neutral color.