A collisional-radiative model describing non-local-thermodynamic-equilibrium plasmas is developed. It is based on the HULLAC suite of codes for the transitions rates, in the zero-temperature radiation field hypothesis. Two variants of the model are presented, the first one is configurationaveraged, while the second one is a detailed level version. Comparisons are made between them in the case of a carbon plasma; they show that the configuration-averaged code gives correct results for an electronic temperature T e = 10 eV (or higher) but fails at lower temperatures such as T e = 1 eV. The validity of the configuration-average approximation is discussed: the intuitive criterion requiring that the average configuration-energy dispersion must be less than the electron thermal energy turns out to be a necessary but far from sufficient condition. Another condition based on the resolution of a modified rate-equation system is proposed. Its efficiency is emphasized in the case of low-temperature plasmas. Finally, it is shown that near-threshold autoionization cascade processes may induce a severe failure of the configuration-average formalism. It is now well-known that in highly-charged hot plasmas, emission and absorption spectra usually display broad structures theoretically described as unresolved transition arrays (UTA) [1,2,3], spin-orbit split arrays (SOSA) [4] or supertransition arrays (STA) [5]. Isolated lines may also be present when transitions occur between two configurations of small degeneracy. The UTA formalism consists in expanding the individual transition energies as a function of the various moments < E n > -where the ponderation is performed using line strengths -with the assumption that levels inside a given configuration are distributed according to thermal equilibrium, the validity of this assumption lying on the condition that the configuration width ∆ c must be smaller than the thermal energy k B T e . Due to its numerous applications, the theory of non-LTE plasmas is nowadays a very active subject [19,20]. For instance, laser-produced and discharged-produced plasmas appear as very promising sources of intense extreme-UV light well suited for 13.5 nm-lithography ([21, 22, 23] and other references in the same volume); for such plasmas of moderate density, the non-LTE condition prevail in most cases. Another domain of application is low-density astrophysics plasmas as well as laboratory coronal plasmas.The aim of this paper is first to present a detailed CR model. One essential feature is that it must be based on a reliable atomic code. To this respect, the HULLAC (Hebrew University Lawrence Livermore Atomic Code) parametric-potential code is known to be efficient in applications dealing with ion spectroscopy and collisional rate calculation. A known limitation of several atomic models used in plasma physics [12,13,14,16,17] is that configuration interaction is ignored. However it has been demonstrated that configuration interaction may play a major role in several radiative effects in pla...