The partial structure factors pertaining to DNA-DNA, DNA-polyamine, and polyamine-polyamine density correlations in DNA fragment (contour length 54 nm) solutions have been measured with small angle neutron scattering and contrast matching in water. The effect of the polyamines putrescine and spermidine on the DNA molecular structure is gauged from the limiting behavior of the DNA-DNA partial structure factor at high values of momentum transfer. The double layer structure and the extent to which the polyamines can approach the DNA are derived from the DNA-polyamine and polyamine-polyamine partial structure factors. For this purpose, the structure factors are interpreted with the correlation functions derived from the classical Poisson-Boltzmann and the modified Poisson-Boltzmann equations and/or Monte Carlo simulation. For simple salt free DNA with tetramethylammonium or putrescine counterions, spatial fluctuations in the charge density are discussed in terms of the charge structure factor. The structural arrangement of putrescine and spermidine can be fully rationalized in terms of their valence. In the case of spermidine, it is necessary to include ionic correlation effects, but this could be accomplished by modeling the ligands as hard spheres. The polyamines have no detectable effect on the DNA molecular structure and are too large to penetrate the grooves to any significant extent. These results imply that DNA condensation in the presence of polyamines is largely governed by electrostatic interactions, rather than by the binding of the multivalent cation per se.