  We study the effects of the ionizing and dissociating photons produced by
PopIII objects on the surrounding intergalactic medium. We find that the
typical size of a H_2 photodissociated region, R_d ~ 1-5 kpc, is smaller than
the mean distance between sources at z ~ 20-30, but larger than the ionized
region by a factor depending on the detailed properties of the emission
spectrum. This implies that clearing of intergalactic H_2 occurs before
reionization of the universe is complete. In the same redshift range, the
soft-UV background in the Lyman-Werner bands, when the intergalactic H and H_2
opacity is included, is found to be J_LW ~ 1d-30 - 1d-27 erg cm^{-2} s^{-1}
Hz^{-1}. This value is well below the threshold required for the negative
feedback of PopIII objects on the subsequent galaxy formation to be effective
in that redshift range.
