  Due to the complexity of modeling the radiative transfer inside the accretion
columns of neutron star binaries, their X-ray spectra are still commonly
described with phenomenological models, for example, a cutoff power law. While
the behavior of these models is well understood and they allow for a comparison
of different sources and studying source behavior, the extent to which the
underlying physics can be derived from the model parameters is very limited.
During recent years, several physically motivated spectral models have been
developed to overcome these limitations. Their application, however, is
generally computationally much more expensive and they require a high number of
parameters which are difficult to constrain. Previous works have presented an
analytical solution to the radiative transfer equation inside the accretion
column assuming a velocity profile that is linear in the optical depth. An
implementation of this solution that is both fast and accurate enough to be
fitted to observed spectra is available as a model in XSPEC. The main
difficulty of this implementation is that some solutions violate energy
conservation and therefore have to be rejected by the user. We propose a novel
fitting strategy that ensures energy conservation during the
$\chi^2$-minimization which simplifies the application of the model
considerably. We demonstrate this approach as well a study of possible
parameter degeneracies with a comprehensive Markov-chain Monte Carlo analysis
of the complete parameter space for a combined NuSTAR and Swift/XRT dataset of
Cen X-3. The derived accretion-flow structure features a small column radius of
$\sim$63 m and a spectrum dominated by bulk-Comptonization of bremsstrahlung
seed photons, in agreement with previous studies.
