Various aspects of infrared radiative transfer through clouds are investigated. First, three solutions, all utilizing the absorption approximation method, corresponding to different assumptions of the optical depth dependence on the source function (Planck function) are discussed and evaluated. It is shown that the difference in results between the solutions with linear and exponential dependence on the source function is small under the usual vertical resolution condition in climate models. Second, a new approach to the perturbation method for cloud scattering is presented. This scheme follows the standard perturbation method procedure. In this work, the perturbation is applied such that the zeroth-order equation pertains to the absorption approximation. This enables an accurate treatment of cloud scattering and allows for an improved and consistent treatment of absorbing aerosols layers in the absence of cloud. This new scheme is simpler and more efficient compared to the old perturbation method for infrared scattering. Last, a general method is devised for calculating the random, maximum, and slant-wise overlap of cloud layers. The method integrates conveniently into the two-stream radiative transfer scheme used in this work. For several random cloud cases and maximum (or slant-wise) overlap cloud cases with large variation in fractional cloud amounts, the error in the cooling rate is generally smaller than 1 K/day, and the error in the radiative flux is generally smaller than 3 Wm-2$