An improved method of applying exponential sum fitting transmissions (ESFT) to inhomogeneous atmospheres (referred to as inhomogeneous ESFT or IESFT) is presented, and its use in a broadband radiative transfer model is documented. Instead of using a scaling function to represent the pressure and temperature dependence of the absorption coefficient we apply the ESFT to all pressures and temperatures based on weight terms determined at reference conditions. The exponential terms corresponding to all pressures and temperatures form a look-up table which can be used to interpolate to the corresponding value at the real pressure and temperature. The IESFT is performed using a nonlinear least squares routine with some constraints to ensure that the ranking of the exponential terms is maintained. The method is tested against line-by-line calculations, and the results show that the use of IESFT in the two stream approximation of radiative transfer can reduce the cooling rate error by a factor of 2 relative to the use of a scaling function, particularly in the upper atmosphere. An application of the treatment of overlapping gaseous absorption developed by Mlawer et al. <1997> to ESFT is described. The basic idea of this method is to treat the mixture of two absorbing gases as a single gas by introducing a binary interpolation parameter which reflects the relative abundance of the two designated gases. Tests against line-by-line calculations show that this method is not only accurate but also computationally efficient. ¿ 1999 American Geophysical Union