We have generalized and substantially improved our previous calculations of radiative shocks in pregalactic gas. We have solved the hydrodynamical conservation equations, along with the rate equations for nonequilibrium ionization, recombination, and molecule formation and the equation of radiative transfer, for steady state shocks in a gas of primordial composition. Such shock waves are relevant to a wide range of theories of galaxy and pregalactic star formation. Our calculation self-consistently includes the effects of the diffuse postshock emission as well as a possible external radiation flux on the postshock flow and the preshock ionization levels. We confirm our previous result that the shocked gas cools faster than it can recombine and, as a result, is able to form an H-2 concentration as high as 10(-3) via the formation of H- and H2+ intermediaries due to the enhanced nonequilibrium ionization fraction at 10(4) K. With such an H-2 concentration, the gas cools by rotational-vibrational line excitation of H-2 molecules to well below the canonical final temperature of 10(4) K for a molecule-free gas without metals. This cooling below 10(4) K significantly lowers the characteristic gravitational fragment mass estimated for shocks relative to the value if the gas cooling stops at 10(4) K. We show that, as the level of the external radiation flux is increased, the formation of and cooling by H-2 molecules can be inhibited and delayed. Finally, the detailed radiation spectra and ionizing photon number fluxes emergent from these shocks are presented.