The partial and charge structure functions of 163 base-pairs DNA fragment solutions are experimentally determined by small-angle neutron scattering at a relatively low concentration of 0.05 M nucleotides/L. In the momentum transfer range q > 0.05 Angstrom(-1), the data agree with theoretical model calculations according to the cell model together with a distribution for the counterions around the rodlike DNA fragment obtained from the Poisson-Boltzmann equation. For q > 0.075 Angstrom(-1), the scattered intensities agree with previous results on similar, but higher concentrated (i.e., 0.1 M nucleotides/L) solutions [van der Maarel; et al. J. Phys. II (France) 1992, 2, 109]. Unlike the previous data, the present results can be compared with the theoretical curves up to sufficiently low q values to check the theoretically expected low q upward curvature of the monomer-counterion and the counterion-counterion structure functions. A shell-like step radial counterion distribution as well as a model in which the condensed counterions are uniformly distributed within a cylindrical volume including the DNA molecule are checked and found to be in disagreement with the experimental data.