We present radio, optical and X-ray detected counterparts to the sub-mm sources found using SCUBA in the Hubble Deep Field North region (GOODS-N). A new counterpart identification statistic is developed to identify properties of galaxies detected at other wavelengths that can be used to aid counterpart identification. We discriminate between criteria that can be used to pre-select sub-mm bright objects, and those that identify the counterpart to a known sub-mm object. Optically faint galaxies detected in the deepest 1.4 GHz radio continuum maps are the only effective way of pre-selecting SCUBA galaxies, and radio sources are the best way to identify counterparts to known sub-mm detections. Looking at radio spectral indices, only the steeper sources (indicative of star formation) are detected in the sub-mm. Although we find several X-ray identifications, we show that deep Chandra images do not contribute to counterpart identifications, since in all cases they are already detected in the more easily obtained VLA radio maps. We also find find no evidence for clustering between Chandra and SCUBA sources in this field. For a known SCUBA position, the reddest source tends to be the correct association, although we can find no cut on colour, magnitude, or clustering property that efficiently pre-selects for SCUBA sources. 15 micron ISO sources are statistically detected by SCUBA, but the limiting mid-IR flux is not low enough to provide useful constraints. We present postage stamp strips for each SCUBA detection in separate bands from X-ray to radio, providing direct visual evidence that approximately half of the sub-mm sources in this field remain unidentified, despite an abundance of deep multi-wavelength data.
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