The polyamines spermidine, spermine and putrescine are now known to induce tertiary collapse of DNA. In this collapsed state DNA assumes a compact toroidal conformation. However, the structural details of DNA in these compact particles and the forces that stabilize the collapsed state are not clear. We show here that the structural arrangement of DNA in this tertiary conformation is determined by the chemical structure of the agent used to collapse. We have used aliphatic triamines (NH+3--(CH2)3--NH+2--(CH2)n--NH+3 with n = 3, 4, 5 and 8) and diamines (NH+3--(CH2)x--NH+3 with x = 2, 3, 4 and 6) to collapse DNA. We find that the Bragg spacing and the calculated interhelical spacing for a hexagonal packing model vary systematically with the length of the methylene bridge. We also find that the ionic strength of the solution has no effect on the Bragg spacing. This observation suggests that the arrangement of DNA strands in the complexes is determined by the structure of the polycation, and argues against suggestions that the structure of the collapsed state is maintained by the balance of long-range electrostatic repulsive and attractive forces. Instead we propose that DNA helices form a hexagonal array with counterions in the interstices between the helices resulting in a stable three-dimensional phase with high structural order. Arguments are presented favoring such a model in terms of stabilizing and destabilizing thermodynamic forces.