  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).
