We present millimeter wavelength detections of three faint sources that are
most likely high-redshift starburst galaxies. For one of the sources, whic
h 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 unr
esolved 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 sou
rces were discovered in a deep 250 GHz (1.2 mm) survey with the Max-Planck
Millimeter Bolometer (MAMBO) array at the IRAM 30 m telescope. Both have fl
uxes of approximate to 4 mJy and radio counterparts with a 1.4 GHz flux den
sity of approximate to 75 mu Jy. Their radio-to-mm flux ratios suggest reds
hifts larger than 2. Both sources are faint in the optical and near-infrare
d, one showing a 20.5 mag K-band counterpart. From our data and that availa
ble 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 like
ly to be at z > 2.