We present millimeter wavelength detections of three faint sources that are most likely high-redshift starburst galaxies. For one of the sources, which was previously discovered with SCUBA at 850 mu m, we present a detection with the IRAM interferometer at 240 GHz (1.25 mm) that shows the object unresolved at an angular resolution of 2.5, and coincident within 1 with a radio source and a galaxy detected in the near-infrared. The two other sources were discovered in a deep 250 GHz (1.2 mm) survey with the Max-Planck Millimeter Bolometer (MAMBO) array at the IRAM 30m telescope. Both have fluxes of ~4 mJy and radio counterparts with a 1.4 GHz flux density of ~75 muJy. Their radio-to-mm flux ratios suggest redshifts larger than 2. Both sources are faint in the optical and near-infrared, one showing a 20.5 mag K-band counterpart. From our data and that available in the literature, we estimate the redshift distribution of twenty-two faint mm and sub-mm sources and conclude that the majority of them are likely to be at z>2.
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