The morphological description of fractal agglomerates is generally reduced to only two parameters,namely the mass fractal dimension and its prefactor. In the most evolved approaches, a stretching exponent is also introduced, while a packing factor is preferred to the fractal prefactor. In any case, the current analytical description of agglomerates morphology is accurate only for sufficiently large agglomerates, which is due to the limited spatial extension of the clusters that are actually quasi-fractal. In the present study, a cutoff function of the pair correlation function is considered for both larger and smaller scales. This enables a more accurate morphological description valid for any cluster size is to be given taking into account the polydispersity of the primary spheres. This new analytical morphological description relying on 5 parameters, is presented here for the first time. The physical range covered by these morphological parameters is determined based on virtually generated Diffusion Limited Cluster Agglomeration. Finally, the model is used to express the fractal prefactor and structure factors and their dependence on agglomerate size and morphological parameters is investigated.