  We present spectroscopic X-ray data of two candidate ultra-compact X-ray
binaries: 4U~0614+091 and 4U~1543$-$624. We confirm the presence of a broad O
VIII Ly$\alpha$ reflection line (at $\approx18\ \AA$) using {\it XMM-Newton}
and {\it Chandra} observations obtained in 2012 and 2013. The donor star in
these sources is carbon-oxygen or oxygen-neon-magnesium white dwarf. Hence, the
accretion disc is enriched with oxygen which makes the O VIII Ly$\alpha$ line
particularly strong. We also confirm the presence of a strong absorption edge
at $\approx14$ \AA\ so far interpreted in the literature as due to absorption
by neutral neon in the circumstellar and interstellar medium. However, the
abundance required to obtain a good fit to this edge is $\approx3-4$ times
solar, posing a problem for this interpretation. Furthermore, modeling the
X-ray reflection off a carbon and oxygen enriched, hydrogen and helium poor
disc with models assuming solar composition likely biases several of the
best-fit parameters. In order to describe the X-ray reflection spectra
self-consistently we modify the currently available {\sc xillver} reflection
model. We present initial grids that can be used to model X-ray reflection
spectra in UCXBs with carbon-oxygen-rich accretion disc. We find that the new
reflection model provides a better overall description of the reflection
spectra of 4U~0614+091 and 4U~1543$-$624 than the reflection models that assume
solar abundances. Besides a strong O VIII Ly$\alpha$ line the new reflection
model also shows a strong O VIII K-edge (at $14.23$ \AA). We find that the
absorption edge at $\approx 14$ \AA\ present in the data can be described by a
O VIII K-edge formed due to reflection in the accretion disc and a Ne I K-edge
originating mostly in the interstellar medium, mitigating the problem of the
apparent very high neon abundance.
