We derive general expressions for the efficiency of cw phase conjugation by degenerate four-wave mixing and for the power ${P}_{\mathrm{cr}}$ for cw self-trapping of coherent electromagnetic beams in fluids and glasses in which these effects arise predominantly from driven nuclear motions (molecular vibrations, molecular reorientation, elastic deformations, etc.). Apart from their dependence on beam frequency \ensuremath{\omega}, medium temperature T, and refractive index n, these expressions are functions only of the integrated (polarized and depolarized) light scattering strengths versus scattering angle in the medium and the attenuation coefficient \ensuremath{\alpha}. There is no other dependence on the scattering mechanism. When attenuation is entirely due to scattering, the expressions simplify and suggest that unprecedented low powers (in the microwatt regime for microwaves) can produce self-focusing and strong phase conjugation, as well as other beam mixing effects, when beam geometries are optimized in the scattering medium. In this case we find, for example, ${P}_{\mathrm{cr}}$\ensuremath{\sim}${\mathrm{nk}}_{B}$T${\ensuremath{\omega}}^{2}$/c\ensuremath{\alpha} (${\mathrm{k}}_{\mathrm{B}}$ is Boltzmann's constant and c is the velocity of light) provided that there is significant beam diffraction in length ${\ensuremath{\alpha}}^{\mathrm{\ensuremath{-}}1}$. Our results also apply to some other media such as electron plasma.