Glass is provided so as to have high visible transmission and/or fairly clear or neutral color. In certain example embodiments of making glass according to examples of the invention, the glass batch may include a base glass (e.g., soda lime silica base glass) and, in addition, by weight percentage: total iron (expressed as Fe₂O₃):  0.01 to 0.30% erbium oxide (e.g., Er₂O₃):  0.01 to 0.30% cerium oxide (e.g., CeO₂): 0.005 to 0.30%.

Optionally, neodymium oxide (e.g., Nd₂O₃) may also be provided in the glass in certain example embodiments. In other embodiments, the cerium oxide may be replaced with or supplemented by NaNO₃ or some other nitrate(s) as an oxidizer.