Sequences of guanines, GG and GGG, are known to be readily oxidized, forming radical cations, i.e., hole traps, on DNA. The trapping probability of GG is less than that of GGG. Lewis et al. (J. Am. Chem. Soc. 2000, 122 12037) have used measurements on synthetic hairpins to determine the free energy liberated when a hole goes from the radical cation G(+) to GG or to GGG. They find these free energies to be of the order of thermal energy at room temperature, in contradiction to the expectation by many of much greater trap depths. We have calculated the wave function of a hole on G, on GG. and on GGG surrounded by adenines, as in the Lewis et al. experiments, using a simple tight-binding model. We find that to account for the shallow traps found by them it is necessary that the difference in ionization potentials of contiguous guanine and adenine be smaller by about 0.2 eV than the 0.4 eV found for isolated bases. Using this value and taking into account polaron formation. we find the wave functions of holes trapped on G. GG, or GGG to extend over similar to6 sites (bases) and with energy level differences in good agreement with the values found by Lewis et al.