Variational computations of the binding energy per particle for various models of nuclear matter are reported. The main purpose is to compare the results corresponding to a «semi-crystallic» structure characterized by correlated density fluctuations of the four spin-isospin nucleon types, with those corresponding to the standard «Fermi gas» homogeneous and isotropic nuclear-matter structure. It is found that, in some cases, the semicrystallic configuration yields more overall attraction (actually less overall repulsion) than the Fermi-gas case, already at (mean) nuclear densities equal to the central density of ordinary (heavy) nuclei. This effect becomes more pronounced at higher (mean) nuclear densities; it can, in most cases, be attributed, at least in part, to the tensor component of the nuclear interaction, that averages to zero in the Fermi-gas case, and yields instead an attractive contribution in configurations with appropriately correlated density fluctuations of the four spin-isospin nucleon states. All computations are based on realistic one-boson exchange nucleon-nucleon potentials. The correlations associated with the strongly repulsive character of the nucleon-nucleon interaction at short range have not been properly accounted for. The results of this paper have therefore no immediate phenomenological implications; whether the effect displayed here is preserved when the repulsive core of the nucleon-nucleon interaction is properly taken into account (both in the computations with and without density fluctuations) remains an open question.