  ALMA observations have revealed that [CII] 158$\mu$m line emission in high-z
galaxies is ~2-3$\times$ more extended than the UV continuum emission. Here we
explore whether surface brightness dimming (SBD) of the [CII] line is
responsible for the reported [CII] deficit, and the large $L_{\rm
[OIII]}/L_{\rm [CII]}$ luminosity ratio measured in early galaxies. We first
analyse archival ALMA images of nine z>6 galaxies observed in both [CII] and
[OIII]. After performing several uv-tapering experiments to optimize the
identification of extended line emission, we detect [CII] emission in the whole
sample, with an extent systematically larger than the [CII] emission. Next, we
use interferometric simulations to study the effect of SBD on the line
luminosity estimate. About 40% of the extended [CII] component might be missed
at an angular resolution of 0.8$^{\prime\prime}$, implying that $L_{\rm [CII]}$
is underestimated by a factor $\approx2$ in data at low (<7) signal-to-noise
ratio . By combining these results, we conclude that $L_{\rm [CII]}$ of z>6
galaxies lies, on average, slightly below the local $L_{\rm [CII]}-SFR$
relation ($\Delta^{z=6-9}=-0.07\pm0.3$), but within the intrinsic dispersion of
the relation. SBD correction also yields $L_{\rm [OIII]}/L_{\rm [CII]}<10$,
i.e. more in line with current hydrodynamical simulations.
