We have discovered three very faint carbon stars (m V >19) in the course of a multicolour survey for high-redshift quasars. Proper motion measurements have been made of these stars to determine their luminosity class. On this basis, the star 0045-259 is confirmed as a halo dwarf, joining the four dwarf carbon stars already known. These five dwarfs appear to have similar absolute magnitudes and tangential velocities. A second star, 0041 - 295, is also a dwarf, yet either its absolute magnitude or its tangential velocity differs from those of the five other dwarfs; it may be the first disc dwarf carbon star found. The time baseline for the proper motion measurement for the third star, 2048-48, is too small to allow the luminosity class to be determined