  The derivation of abundances in gaseous nebulae ionised by massive stars
using optical collisionally excited emission lines is studied in this work
comparing the direct or $T_e$ method with updated grids of photoionisation
models covering a wide range of input conditions of O/H and N/O abundances and
ionisation parameter. The abundances in a large sample of compiled objects with
at least one auroral line are re-derived and later compared with the $\chi^2$
weighted-mean abundances from the models. The agreement between the abundances
using the two methods both for O/H and N/O is excellent with no additional
assumptions about the geometry or physics governing the HII regions. Although
very inaccurate model-based O/H are obtained when no auroral lines are
considered, this can be overcome assuming empirical laws between O/H, log $U$,
and N/O to constrain the considered models. In this way, for 12+log(O/H) $>$
8.0, a precision better than 0.1dex consistent with the direct method is
attained. For very low-$Z$, models give higher O/H values and a high
dispersion, possibly owing to the contamination of the low-excitation
emission-lines. However, in this regime, the auroral lines are usually
well-detected. The use of this procedure, in a publicly available script,
HII-CHI-mistry}, leads to the derivation of abundances in faint/high redshift
objects consistent with the direct method based on CELs.
