A strategy for achieving negative phase velocity (NPV) in a homogenized composite material (HCM) involves constituent material phases that do not support NPV propagation. The HCM and its constituent phases are isotropic dielectric-magnetic materials. The real parts of their permittivities are negative-valued whereas the real parts of their permeabilities are positive-valued (or vice versa). The constituent material phases are randomly distributed as spherical particles. The Bruggeman homogenization formalism indicates that the HCM can support NPV propagation, the extended Bruggeman homogenization formalism suggests that increasing the dimensions of the constituent particles diminishes the scope for NPV propagation in the HCM, and the strong-permittivity-fluctuation theory further shows that the propensity of the HCM to support NPV propagation is sensitive to the distributional statistics of the constituent material particles and diminishes as the correlation length increases.