  We present a first study based on the analysis of the DEep Spectra of Ionized
REgions Database (DESIRED). This is a compilation of 190 high signal-to-noise
ratio optical spectra of HII regions and other photoionized nebulae, mostly
observed with 8-10m telescopes and containing $\sim$29380 emission lines. We
find that the electron density --$n_{\rm e}$-- of the objects is underestimated
when [SII] $\lambda6731/\lambda6716$ and/or [OII] $\lambda3726/\lambda3729$ are
the only density indicators available. This is produced by the non-linear
density dependence of the indicators in the presence of density
inhomogeneities. The average underestimate is $\sim 300$ cm$^{-3}$ in
extragalactic HII regions, introducing systematic overestimates of $T_{\rm
e}$([OII]) and $T_{\rm e}$([SII]) compared to $T_{\rm e}$([NII]). The
high-sensitivity of [OII] $\lambda\lambda7319+20+30+31/\lambda\lambda3726+29$
and [SII] $\lambda\lambda4069+76/\lambda\lambda6716+31$ to density makes them
more suitable for the diagnosis of the presence of high-density clumps. If
$T_{\rm e}$([NII]) is adopted, the density underestimate has a small impact in
the ionic abundances derived from optical spectra, being limited to up to
$\sim$0.1 dex when auroral [SII] and/or [OII] lines are used. However, these
density effects are critical for the analysis of infrared fine structure lines,
such as those observed by the JWST in local star forming regions, implying
strong underestimates of the ionic abundances. We present temperature relations
between $T_{\rm e}$([OIII]), $T_{\rm e}$([ArIII]), $T_{\rm e}$([SIII]) and
$T_{\rm e}$([NII]) for the extragalactic HII regions. We confirm a non-linear
dependence between $T_{\rm e}$([OIII])-$T_{\rm e}$([NII]) due to a more rapid
increase of $T_{\rm e}$([OIII]) at lower metallicities.
