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We report the discovery of four short-period eclipsing systems in the Keplerlight 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. Thesystems show BEaming, Ellipsoidal and Reflection (BEER) phase modulationstogether with primary and secondary eclipses. These add to the 6 Kepler and 18WASP short-period eclipsing dA+WD binaries that were previously known. Thelight curves, together with follow-up spectroscopic observations, allow us toderive the masses, radii, and effective temperatures of the two components ofthe four systems. The orbital periods, of 1.17-3.82 days, and WD masses, of0.19-0.22 Msun, are similar to those of the previously known systems. The WDradii of KOI-3818, KIC 2851474, and KIC 9285587 are 0.026, 0.035, and 0.026Rsun, respectively, the smallest WD radii derived so far for short-periodeclipsing dA+WD binaries. These three binaries extend the previously knownpopulation to older systems with cooler and smaller WD secondaries. KOI-3818displays evidence for a fast-rotating primary and a minute but significanteccentricity of ~0.0015. These features are probably the outcome of themass-transfer process.

BEER analysis of Kepler and CoRoT light curves: IV. Discovery of four new low-mass white dwarf companions in the Kepler data