Twelve new absorption bands of the iodine molecular spectrum belonging to the (0, upsilon double prime ), (1, upsilon double prime ) and (2, upsilon double prime ) progressions, where 10 less than equivalent to upsilon double prime less than equivalent to 14, were analyzed. The data obtained by Fourier spectroscopy measurements between 12 600 and 14 000 cm** minus **1, permit both the extension of the precise determination of the molecular constants G( upsilon double prime ), B( upsilon double prime ) and D( upsilon double prime ) of the ground state X(**1 SIGMA //g** plus ) up to upsilon double prime equals 14 and studies of the low-lying levels of the excited state B(**3 PI //o//u** plus ); in particular the separation between the two states X and B is found to be T//0//,//0 equals 15 724. 586 plus or minus 0. 003 cm** minus **1. Rotational distortion D, H and L constants for the B and X states have been computed from RKR potentials according to the method of Albritton et al. (J. Mol. Spectrosc. 46 (1973) 25). Good agreement between experimental and calculated D( upsilon double prime 41 ) and D( upsilon prime ) values was found. Franck-Condon Factors (FCF) were calculated and the computed relative intensities are consistent with the observed ones.