Absolute wave-number measurements, with an accuracy of 2-11 parts in 10(9), are presented for 27 (127)I(2) hyperfine-structure lines in the range 5763-6563 A. Individual components were resolved by saturation spectroscopy and their wave numbers measured by a comparison with wavelength standards made using a temperature-stabilized Fabry-Perot interferometer. Good consistency is found among the four accepted (127)I(2)wavelength standards. The result of a previous measurement at 6563 A, which was used as the basis for a Rydberg-constant determination, is also confirmed.