We model the velocity-fields using the [GalPak3D]{} software [@Bouche2015]. [GalPak3D]{} uses a Monte-Carlo approach to extract the kinematic and morphological parameters from three-dimensional image cubes, accounting for both the spatial and spectral response of the instrument, assuming a parametric model for a rotating disc. For our simulations, we assume an exponential disc profile - an appropriate choice for ALESS SMGs, which show a mean Sérsic index of $n=0.9\pm0.2$ (@Hodge2016, $n=1$ corresponds to an exponential profile.). To improve the SNR and the speed of the calculations, we re-sampled our data onto cubes with a pixel size of 25 mas, using natural weighting.

Figure \[fig:galpak\] shows the input and reconstructed moment-0 and moment-1 maps for ALESS 49.1 and 57.1. At the SNR of our Band 8 observations, velocity fields in both sources are consistent with an ordered, disc-like rotation. The deconvolved \[\] rotational curves are shown in Figure\[fig:rot\_curves\], which also lists the FWHM velocity measurements obtained from the fitting of the spatially-integrated CO(3–2) spectra [@CR18]. The source inclinations are inferred by fitting the moment-0 map and agree with those derived from CO(3–2) imaging by @CR18 within 1–2$\sigma$ uncertainty.

![image](aless_galpak.png){width="18.0cm"}\

[@ll|cc @]{} Source & & ALESS 49.1 & ALESS 57.1\
&\
$L_{3-2000 \mathrm{\mu 