We investigate the potential of submm-mm and submm-mm-radio photometric redshifts using a sample of mm-selected sources as seen at 250, 350 and 500 {mu}m by the SPIRE instrument on Herschel. From a sample of 63 previously identified mm-sources with reliable radio identifications in the GOODS-N and Lockman Hole North fields 46 (73 per cent) are found to have detections in at least one SPIRE band. We explore the observed submm/mm colour evolution with redshift, finding that the colours of mm-sources are adequately described by a modified blackbody with constant optical depth {tau} = ({ u}/{ u}0)^{beta} where {beta} = +1.8 and { u}0 = c/100 {mu}m. We find a tight correlation between dust temperature and IR luminosity. Using a single model of the dust temperature and IR luminosity relation we derive photometric redshift estimates for the 46 SPIRE detected mm-sources. Testing against the 22 sources with known spectroscopic, or good quality optical/near-IR photometric, redshifts we find submm/mm photometric redshifts offer a redshift accuracy of |z|/(1+z) = 0.16 (< |z| >= 0.51). Including constraints from the radio-far IR correlation the accuracy is improved to |z|/(1 + z) = 0.15 (< |z| >= 0.45). We estimate the redshift distribution of mm-selected sources finding a significant excess at z > 3 when compared to ~ 850 {mu}m selected samples.
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