Polyamines have important roles in the modulation of the cellular function and are ubiquitous in cells. The polyamines putrescine2+, spermidine3+, and spermine4+ represent the most abundant organic counterions of the negatively charged DNA in the cellular nucleus. These polyamines are known to stabilize the DNA structure and, depending on their concentration and additional salt composition, to induce DNA aggregation, which is often referred to as condensation. However, the modes of interactions of these elongated polycations with DNA and how they promote condensation are still not clear. In the present work, atomistic molecular dynamics (MD) computer simulations of two DNA fragments surrounded by spermidine3+ (Spd3+) cations were performed to study the structuring of Spd3+ “caged” between DNA molecules. Microsecond time scale simulations, in which the parallel DNA fragments were constrained at three different separations, but allowed to rotate axially and move naturally, provided information on the conformations and relative orientations of surrounding Spm3+ cations as a function of DNA-DNA separation. Novel geometric criteria allowed for the classification of DNA-Spd3+ interaction modes, with special attention given to Spd3+ conformational changes in the space between the two DNA molecules (caged Spd3+). This work shows how changes in the accessible space, or confinement, around DNA affect DNA-Spd3+ interactions, information fundamental to understanding the interactions between DNA and its counterions in environments where DNA is compacted, e.g. in the cellular nucleus.