Hepatitis B Virus (HBV) cores assemble on viral RNA, which is reverse transcribed within the core to the partially dsDNA genome of mature HBV. However, constraining dsDNA, a stiff polymer, within a core necessarily requires far greater capsid stability than constraining ssRNA. We hypothesized that, unlike ssRNA, dsDNA would be a poor substrate for assembly. We examined titrations of ssDNA and dsDNA with purified HBV core protein, Cp183, by EMSA, EM, DLS, and etheno-DNA fluorescence. Cp183 bound ssDNA with high affinity to form virus-like capsids. However, Cp183 bound dsDNA poorly, forming a mixture of irregular complexes. Nonetheless, we observed some normal cores in dsDNA assembly reactions, indicating that the energy required to bend DNA could be similar to the protein–protein association energy. This similarity of energies suggests that dsDNA stresses mature HBV cores, in agreement with calculation, which may be the basis for the virus maturation signal and DNA release.