  We present radial velocity observations of four binary white dwarf candidates
identified through their over-luminosity. We identify two new double-lined
spectroscopic binary systems, WD 0311-649 and WD 1606+422, and constrain their
orbital parameters. WD 0311-649 is a 17.7 h period system with a mass ratio of
$1.44 \pm 0.06$ and WD 1606+422 is a 20.1 h period system with a mass ratio of
$1.33 \pm 0.03$. An additional object, WD 1447-190, is a 43 h period
single-lined white dwarf binary, whereas WD 1418-088 does not show any
significant velocity variations over timescales ranging from minutes to
decades. We present an overview of the 14 over-luminous white dwarfs that were
identified by Bedard et al., and find the fraction of double- and single-lined
systems to be both 31%. However, an additional 31% of these over-luminous white
dwarfs do not show any significant radial velocity variations. We demonstrate
that these must be in long-period binaries that may be resolved by Gaia
astrometry. We also discuss the over-abundance of single low-mass white dwarfs
identified in the SPY survey, and suggest that some of those systems are also
likely long period binary systems of more massive white dwarfs.
