Absorption spectra of Cu⁺ and Cu²⁺ were measured for silicate, borate, and phosphate glasses doped with 0.1 mol%Cu₂O. The molar extinction coefficient at the peak wavelength of the ²B_1g→²B_2g transition of Cu²⁺ was used as a parameter showing the relative content of Cu⁺ ions in glass samples. Compositional dependence of Cu⁺-Cu²⁺ redox was examined using compositional parameter B which represented the average basicity of glasses. We estimated that glass composition within the B range of 0.2-0.3 is suited for Cu⁺-doped tunable glass laser because the absorption of Cu²⁺ was minimized at this range. In borate and phosphate glasses, the Cu⁺ ion was chemically stabilized by the addition of alumina. We concluded that the glass composition suitable for Cu⁺-doped tunable glass laser materials is 10Na₂O·80B₂O₃·10Al₂O₃ on the basis of fluorescence measurement.