We present the results of deep near-infrared spectroscopy of seven submillimetre-selected galaxies from the Submillimetre Common User Bolometer Array (SCUBA) 8-mJy Survey and Canada-UK Deep Submillimetre Survey(CUDSS). These galaxies were selected because they are too faint to be accessible to optical spectrographs on large telescopes. We obtain a spectroscopic redshift for one object, and likely redshifts for two more, based on a combination of marginal emission-line detections and the shape of the continuum. All three redshifts broadly agree with estimates from their radio/submm spectral energy distributions. From the emission-line strengths of these objects, we infer star formation rates of 10(-25) M-circle dot yr(-1), while the lack of detections in the other objects imply even lower rates. By comparing our results with those of other authors, we conclude it is likely that the vast majority (more than 90 per cent) of the star formation in these objects is completely extinguished at rest-frame optical wavelengths, and the emission lines originate in a relatively unobscured region. Finally, we look at future prospects for making spectroscopic redshift determinations of submm galaxies.