  We present high-resolution spectroscopy of two nearby white dwarfs with
inconsistent spectroscopic and parallax distances. The first one, PG 1632+177,
is a 13th magnitude white dwarf only 25.6 pc away. Previous spectroscopic
observations failed to detect any radial velocity changes in this star. Here,
we show that PG 1632+177 is a 2.05 d period double-lined spectroscopic binary
(SB2) containing a low-mass He-core white dwarf with a more-massive, likely
CO-core white dwarf companion. After L 870-2, PG 1632+177 becomes the second
closest SB2 white dwarf currently known. Our second target, WD 1534+503, is
also an SB2 system with an orbital period of 0.71 d. For each system, we
constrain the atmospheric parameters of both components through a composite
model-atmosphere analysis. We also present a new set of NLTE synthetic spectra
appropriate for modeling high-resolution observations of cool white dwarfs, and
show that NLTE effects in the core of the H$\alpha$ line increase with
decreasing effective temperature. We discuss the orbital period and mass
distribution of SB2 and eclipsing double white dwarfs with orbital constraints,
and demonstrate that the observed population is consistent with the predicted
period distribution from the binary population synthesis models. The latter
predict more massive CO + CO white dwarf binaries at short ($<1$ d) periods, as
well as binaries with several day orbital periods; such systems are still
waiting to be discovered in large numbers.
