of star formation. They distinguish between two models of metal-poor narrow-line regions, either in combination with a low-redshift star-forming branch, or with a star-forming branch shifted towards lower \[NII\]/H$\alpha$ values for a given \[OIII\]/H$\beta$ ratio, as found in many actively star-forming galaxies at z$\sim$2 [@erb06b; @lehnert09; @nmfs09; @steidel14].

The \[NII\]/H$\alpha$ ratios of our galaxies fall into the range predicted by the low-metallicity models of @kewley13a, however, the \[OIII\]/H$\beta$ ratios exceed this range by few 0.1 dex. Our data are not sensitive to distinguishing whether the star-forming ISM in our galaxies may be more akin to low-redshift conditions, or the more extreme environs in high-z starburst galaxies. But given the high star formation rates implied by the far-infrared continuum in at least some of our sources [@drouart14], and because the offset of the star formation branch in these galaxies appears to be most likely due to a higher ionization parameter in these galaxies, we suspect that the latter will likely be the case. We will discuss this point further in §\[ssec:metallicity\]

Electron densities {#sssec:densities}
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Amongst the bright rest-frame optical lines, the \[OII\]$\lambda\lambda$3726,3729 and \[SII\]$\lambda\lambda$6716,6731 doublets are particularly interesting, because they provide constraints on the electron density of the warm ionized 