Relative partial photoionization cross-sections and angular distribution parameters, beta, have been measured for the first, I(+)((3)P(2))<--I((2)P(3/2)), and fourth, I(+)((1)D(2))<--I((2)P(3/2)), (5p)(-1) photoelectron (PE) bands of atomic iodine, by performing angle-resolved constant-ionic-state (CIS) measurements on these PE bands in the photon energy range 11.0-23.0 eV. Three Rydberg series, two ns and one nd series, which converge to the I(+) (3)P(1) limit at 11.33 eV and four Rydberg series, two ns and two nd series, which converge to the I(+) (1)D(2) limit at 12.15 eV were observed in the first PE band CIS spectra. The fourth band CIS spectrum showed structure in the 12.9-14.1 eV photon energy range, which is also seen in the first band CIS spectra. This structure arises from excitation to ns and nd Rydberg states that are parts of series converging to the I(+) (1)S(0) limit we reported on earlier, as well as 5s-->5p excitations in the photon energy range 17.5-22.5 eV. These atomic iodine CIS spectra show reasonably good agreement with the equivalent spectra obtained for atomic bromine. The beta-plots for the first PE band recorded up to the I(+) (3)P(1) and I(+) (1)D(2) limits only show resonances corresponding to some of the 5p-->nd excitations observed in the first band CIS spectra scanned to the I(+) (1)D(2) limit (12.15 eV). These plots are interpreted in terms of an angular momentum transfer model with the positive values of beta obtained on resonances corresponding to parity allowed j(t)=1 and 3 channels and the off-resonance negative beta values corresponding to parity unfavored channels, where j(t) is the quantum number for angular momentum transfer between the molecule, and the ion and photoelectron. The beta-plots recorded for iodine are significantly different from those obtained for atomic bromine. Comparison of the experimental CIS spectra and beta-plots with available theoretical results highlights the need for higher level calculations which include factors such as configuration interaction in the initial and final states, relativistic effects including spin-orbit interaction, and autoionization via resonant Rydberg states.