  We present radial velocity observations of four extremely low-mass (0.2 Msol)
white dwarfs. All four stars show peak-to-peak radial velocity variations of
540 - 710 km/s with 1.0 - 5.9 hr periods. The optical photometry rules out
main-sequence companions. In addition, no milli-second pulsar companions are
detected in radio observations. Thus the invisible companions are most likely
white dwarfs. Two of the systems are the shortest period binary white dwarfs
yet discovered. Due to the loss of angular momentum through gravitational
radiation, three of the systems will merge within 500 Myr. The remaining system
will merge within a Hubble time. The mass functions for three of the systems
imply companions more massive than 0.46 Msol; thus those are carbon/oxygen core
white dwarfs. The unknown inclination angles prohibit a definitive conclusion
about the future of these systems. However, the chance of a supernova Ia event
is only 1% to 5%. These systems are likely to form single R Coronae Borealis
stars, providing evidence for a white dwarf + white dwarf merger mechanism for
these unusual objects. One of the systems, SDSS J105353.89+520031.0 has a 70%
chance of having a low-mass white dwarf companion. This system will probably
form a single helium-enriched subdwarf O star. All four white dwarf systems
have unusal mass ratios of < 0.2-0.8 that may also lead to the formation of AM
CVn systems.
