Fast and accurate radiative transfer methods are essential for modeling CO2-rich atmospheres, relevant to the climate of early Earth and Mars, present-day Venus, and some exoplanets. Although such models already exist, their accuracy may be improved as better theoretical and experimental constraints become available. Here we develop a unidimensional radiative transfer code for CO2-rich atmospheres, using the correlated k approach and with a focus on modeling early Mars. Our model differs from existing models in that it includes the effects of CO2 collisional line mixing in the calculation of the line-by-line absorption coefficients. Inclusion of these effects results in model atmospheres that are more transparent to infrared radiation and, therefore, in colder surface temperatures at radiative-convective equilibrium, compared with results of previous studies. Inclusion of water vapor in the model atmosphere results in negligible warming due to the low atmospheric temperatures under a weaker early Sun, which translate into climatically unimportant concentrations of water vapor. Overall, the results imply that sustained warmth on early Mars would not have been possible with an atmosphere containing only CO2 and water vapor, suggesting that other components of the early Martian climate system are missing from current models or that warm conditions were not long lived.