Extracting the shear viscosity of quark-gluon plasma from experimental data has been one of the major goals of heavy-ion physics, leading to very low values of 1-$2/4\pi$. Most of these works have been done using by now outdated EoS parametrizations, and I'll discuss how and whether the use of a contemporary EoS affects the extracted EoS in a full-fledged Bayesian analysis. I will also discuss whether the minimum value of $\eta/s$ depends on how the temperaturedependence of $\eta/s$ is parametrised.