  Core-collapse supernovae (CCSNe) produce large ($\gtrsim 0.1 \, {\rm
M}_\odot$) masses of dust, and are potentially the primary source of dust in
the Universe, but much of this dust may be destroyed before reaching the
interstellar medium. Cassiopeia A (Cas A) is the only supernova remnant where
an observational measurement of the dust destruction efficiency in the reverse
shock is possible at present. We determine the pre- and post-shock dust masses
in Cas A using a substantially improved dust emission model. In our preferred
models, the unshocked ejecta contains $0.6-0.8 \, {\rm M}_\odot$ of $0.1 \,
{\rm \mu m}$ silicate grains, while the post-shock ejecta has $0.02-0.09 \,
{\rm M}_\odot$ of $5-10 {\, {\rm nm}}$ grains in dense clumps, and $2 \times
10^{-3} \, {\rm M}_\odot$ of $0.1 \, {\rm \mu m}$ grains in the diffuse X-ray
emitting shocked ejecta. The implied dust destruction efficiency is $74-94 \%$
in the clumps and $92-98 \%$ overall, giving Cas A a final dust yield of
$0.05-0.30 \, {\rm M}_\odot$. If the unshocked ejecta grains are larger than
$0.1 \, {\rm \mu m}$, the dust masses are higher, the destruction efficiencies
are lower, and the final yield may exceed $0.5 \, {\rm M}_\odot$. As Cas A has
a dense circumstellar environment and thus a much stronger reverse shock than
is typical, the average dust destruction efficiency across all CCSNe is likely
to be lower, and the average dust yield higher. This supports a mostly-stellar
origin for the cosmic dust budget.
