The molecular structures and magnetic properties of six dinitroxide biradicals are described. Five of the dinitroxides are trimethylenemethane-type (TMM-type) biradicals; that is, the intramolecular exchange parameter, J, is modulated by a carbon-carbon double bond. However, the efficacy of the carbon-carbon double bond as an exchange coupler is determined by the molecular conformation. Our results show that the exchange parameters correlate with phenyl-ring torsion angles (phi) via a simple Karplus-Conroy-type relation: J = 44 cos(2) phi - 17. Comparison of these results to those obtained for our isostructural series of bis(semiquinone) biradicals shows that both the magnitude of J and the resistance of ferromagnetic J to bond torsions is proportional to the spin density adjacent to the exchange coupler.