  We report the discovery of four short-period eclipsing systems in the Kepler
light curves, consisting of an A-star primary and a low-mass white dwarf (WD)
secondary (dA+WD) - KIC 4169521, KOI-3818, KIC 2851474, and KIC 9285587. The
systems show BEaming, Ellipsoidal and Reflection (BEER) phase modulations
together with primary and secondary eclipses. These add to the 6 Kepler and 18
WASP short-period eclipsing dA+WD binaries that were previously known. The
light curves, together with follow-up spectroscopic observations, allow us to
derive the masses, radii, and effective temperatures of the two components of
the four systems. The orbital periods, of 1.17-3.82 days, and WD masses, of
0.19-0.22 Msun, are similar to those of the previously known systems. The WD
radii of KOI-3818, KIC 2851474, and KIC 9285587 are 0.026, 0.035, and 0.026
Rsun, respectively, the smallest WD radii derived so far for short-period
eclipsing dA+WD binaries. These three binaries extend the previously known
population to older systems with cooler and smaller WD secondaries. KOI-3818
displays evidence for a fast-rotating primary and a minute but significant
eccentricity of ~0.0015. These features are probably the outcome of the
mass-transfer process.
