The concomitant overabundances of C, N, and s-process elements are commonly ascribed to the complex interplay of nucleosynthesis, mixing, and mass loss taking place in asymptotic giant branch (AGB) stars. At low metallicity, the enhancement of C and/or N can be up to 1000 times larger than the original iron content and significantly affects the stellar structure and its evolution. For this reason, the interpretation of the already available and still growing amount of data concerning C-rich metal-poor stars belonging to our Galaxy as well as to dwarf spheroidal galaxies would require reliable AGB stellar models for low and very low metallicities. In this paper we address the question of calculation and use of appropriate opacity coefficients, which take into account the C enhancement caused by the third dredge-up. A possible N enhancement, caused by the cool bottom process or by the engulfment of protons into the convective zone generated by a thermal pulse and the subsequent huge third dredge-up, is also considered. Based on up-to-date stellar models, we illustrate the changes induced by the use of these opacity coefficients on the physical and chemical properties expected for these stars.