  It is well known that the Soft-Wall holographic model for QCD successfully
reproduces not only the linear Regge spectrum, but also, via the holographic
Wilson confinement criterion, the ''linear plus Coulomb'' confinement potential
similar to the Cornell potential. This property could be interpreted as a
holographic counterpart of the hadron string picture, where the linearly rising
potential and Regge-like spectrum are directly related. However, such a
relation does not take place in the bottom-up holographic approach. Namely, the
Cornell-like potentials arise in a broad class of bottom-up holographic models,
the standard Soft-Wall model is merely a particular representative of this
class. We consider a calculation of confinement potential within a different
representative of this class - a Soft-Wall model with linear dilaton background
in the metric. This model leads to a Hydrogen like spectrum. The calculation of
renormalized potential at short distances turns out to be complicated by a new
subtlety that was skipped in general discussions of the issue existing in the
literature. But the confinement potential of the model is shown to be not very
different from the potential obtained in the standard Soft-Wall model with
quadratic background.
