A dilaton potential is adjusted to recently confirmed lattice QCD thermodynamics data in the temperature range $(0.7 ldots 3.5) T_c$ where $T_c = 155 text{MeV}$ is the pseudo-critical temperature. The employed holographic model is based on a gravity-
-single-field dilaton dual. We discuss conditions for enforcing (for the pure gluon plasma) or avoiding (for the QCD quark-gluon plasma) a first-order phase transition, but still keeping a softest point (minimum of sound velocity).
