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tokens: at the redshifts of interest) and that the seeing was good (0.65 arcsec), slit losses are likely ≲30 per cent. Moreover, because we are primarily concerned with redshifts rather than line luminosities, aperture corrections to the line fluxes are unnecessary. The spectra were obtained using the standard two-position ‘mask nod’ in which the telescope position was dithered ±1.5 arcsec along the slit direction, with individual integration times of 120 s ( H band) or 180 s ( K band). Total integration times of 2880 s were obtained, with 24 and 16 individual exposures in the H and K bands, respectively. The MOSFIRE data were reduced using the publicly available data reduction pipeline developed by the instrument team; 12 see Steidel et al. ( 2014 ) for a detailed description of the procedure. One-dimensional spectra were extracted, flux-calibrated, and analysed using the mospec package (Strom et al. 2017 ). 2.1.2 GNIRS observations Near-infrared spectra of resolved components of two multicomponent single-dish submm sources (UDS292 and UDS306) were obtained using the cross-dispersed mode of the Gemini Near-Infrared Spectrograph (GNIRS 13 ) on the Gemini North 8.1 m telescope. This configuration provides continuous spectral coverage from 0.84 to 2.48 m at a spectral resolution of R ≈ 1500 with a spatial scale of 0.15 arcsec pix −1 . The slit dimensions were 1.0 arcsec × 7.0 arcsec. The observations used an ABBA pattern, nodding along the slit to keep the galaxy on slit at all times. Eight individual on-source integrations of 240 s each were performed for each source. Observations of standard stars were obtained before and after each set of SMG observations. These were used to correct the spectra for telluric absorption. The spectral reduction, extraction, and wavelength and flux calibration procedures were performed using the Gemini iraf package and pyraf . 14 Briefly, the processing consists of removing cosmic ray-like features, dividing by flat-fields taken with infrared and quartz halogen lamps, subtracting sky emission using exposures taken at a different point in the dither pattern, and finally rectifying the tilted, curved spectra using pinhole flats. Wavelength calibration is performed using Argon arc spectra, and then a spectrum of each order is extracted, divided by the standard star observation to cancel telluric absorption lines, and roughly flux-calibrated using the telluric standard star spectrum. The different spectral orders for each extraction window are merged into a single 1D spectrum from 0.84 to 2.48 m. In all cases, the agreement in flux between the overlapping regions of two consecutive orders was very good, and scaling factors of only 3 per cent or less were necessary. 2.1.3 XSHOOTER observations One target was observed on 2015 March 4 with the XSHOOTER echelon spectrograph (Vernet et al. 2011 ) on the ESO VLT-UT2 (Kueyen) as part of programme 094.A-0811(A), providing near-continuous spectroscopy from 0.3 to 2.48 m with a 1.2