The objective of this paper is to present a method that allows simplifying the use of ω-absorption line distribution functions (ω-ALDF) inside rank correlated full-spectrum k-distribution (RCFSK) models for application in combustion problems. In this simplified version, the ω-ALDF is constructed without any a priori information on the problem treated. It can be used directly but, in order to simplify further the concept for possible users, we suggest here approximating this ω-ALDF using an Absorption Line Blackbody Distribution Function (ALBDF) at a temperature defined in terms of the ω-ALDF. The method is validated in some combustion scenarios. The model is assessed by comparison with a narrow band correlated-k (NBCK) model through decoupled radiative simulations of eight turbulent axisymmetric non-premixed jet flames covering a wide range of optical-thicknesses and contributions of soot to radiation. The predictions are within 4 % of the reference solution. A consequence of the proposed approach is that the FSCK parameters, namely the absorption coefficient and the stretching function, depends only on local variables. This allows one to forgo the specification of an arbitrary blackbody source temperature, and to develop a specific storage strategy to provide an efficient model for Computational Fluid Dynamics (CFD) simulations of combustion problems.