The A**3 PI //1//u-X**1 SIGMA //g** plus system of the I//2 molecule, lying in the 9600 minus 8000 A region, has been photographed in absorption under conditions of high dispersion. The band origins and B prime values of 18 bands in the lengthy progressions based on v double prime equals 4 and 5 have been determined. By assuming that the potential curve of the A state is a Morse curve, an estimate of the vibrational numbering of this state has been made. Based on this numbering estimates of important constants of the A**3 PI //1//u state have been achieved: viz. , T//e equals 11,059 cm** minus **1, D//e equals 1488 cm** minus **1, omega //e equals 95. 9 cm** minus **1, Be equals 0. 02817 cm** minus **1, and r//e equals 3. 071 A. A comparison of between the A state and the lower state of the ultraviolet laser transitions of the I//2 molecule, based on the values of the constants D//e, omega //e, chi //e, omega //e, and y//e omega //e, shows that the A state cannot be the lower state of the laser transitions.