An approach to predicting molecular crystal structures, based on systematically searching for densely packed structures within common organic crystal coordination types, followed by lattice energy minimization, has been applied to three planar heterocycles with multiple hydrogen bond donors and accepters, namely, 6-azauracil, uracil, and allopurinol. The dominant electrostatic contribution to the lattice energies was calculated from an ab initio based distributed multipole model of the molecular charge density, providing more confidence that the potential extrapolates correctly to hypothetical crystal structures than is possible with empirical potentials. In all cases, the experimentally observed structure was found, corresponding to the global minimum in the lattice energy. Most of the different possible combinations of hydrogen bonds were found to be able to pack in low-energy crystal structures, with several unknown structures within the energy range associated with possible polymorphism. This raises the question as to what factors, in addition to static lattice energy, need to be considered to predict which crystal structures could be found experimentally.