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

X-ray reflection in oxygen-rich accretion discs of ultra-compact X-ray binaries