  Common envelope (CE) evolution, which is crucial in creating short period
binaries and associated astrophysical events, can be constrained by reverse
modeling of such binaries' formation histories. Through analysis of a sample of
well-constrained white dwarf (WD) binaries with low-mass primaries (7 eclipsing
double WDs, 2 non-eclipsing double WDs, 1 WD-brown dwarf), we estimate the CE
energy efficiency $\alpha_{\rm{CE}}$ needed to unbind the hydrogen envelope. We
use grids of He- and CO-core WD models to determine the masses and cooling ages
that match each primary WD's radius and temperature. Assuming gravitational
wave-driven orbital decay, we then calculate the associated ranges in post-CE
orbital period. By mapping WD models to a grid of red giant progenitor stars,
we determine the total envelope binding energies and possible orbital periods
at the point CE evolution is initiated, thereby constraining $\alpha_{\rm CE}$.
Assuming He-core WDs with progenitors of 0.9 - 2.0 $M_\odot$, we find
$\alpha_{\rm CE} \! \sim \! 0.2-0.4$ is consistent with each system we model.
Significantly higher values of $\alpha_{\rm{CE}}$ are required for higher mass
progenitors and for CO-core WDs, so these scenarios are deemed unlikely. Our
values are mostly consistent with previous studies of post-CE WD binaries, and
they suggest a nearly constant and low envelope ejection efficiency for CE
events that produce He-core WDs.
