The performance and construction of a new algorithm for the calculation of infrared cooling rates and fluxes in terrestrial general circulation models are described in detail. The computational method, which is suitable for use in models of both the troposphere and the middle atmosphere, incorporates effects now known to be important, such an an extended water vapor e-type continuum, careful treatment of water vapor lines, of water-carbon dioxide overlap, and of Voigt line shape. The competing requirements of accuracy and speed are both satisfied by extensive use of a generalization of the simplified exchange approximation of Fels and Schwarzkopf (1975). Cooling rates and fluxes are validated by comparison with benchmark line-by-line calculations on standard atmospheric profiles obtained for the Intercomparison of Radiation Codes Used in Climate Models (ICRCCM). Results indicate that the new algorithm is substantially more accurate than any previously used at the Geophysical Fluid Dynamics Laboratory.