In this article, we compare two analytical methods that have been recently proposed: the columnar density Saha-Boltzmann plot method of Cristoforetti and Tognoni (Cristoforetti, G.; Tognoni, E. Spectrochim. Acta, Part B, 2013, 79-80, 63-71) and the C-sigma model of Aragon and Aguilera (Aragon, C.; Aguilera, J. A. J. Quant. Spectrosc. Radiat. Trans. 2014, 149, 90-102). Both methods are based on the exploitation of self-absorbed lines for the characterization of plasmas in laser-induced breakdown spectroscopy experiments. However, although the two methods can be safely applied in many cases, their usefulness is limited in many practical cases of interest because of the intrinsic constraints of the used plasma model or because of the complexity of the numerical treatment. The two methods are presented here and critically discussed. Finally, an extended C-sigma approach is proposed to merge the advantages of the two methods, overcoming their intrinsic limitations and simplifying the numerical treatment.