A new parametrization for the parton distribution functions with a higher flexibility in the small-$x$ region is presented. It has been implemented in the \texttt{xFitter} open-source PDF fitting tool, and compared to the default \texttt{xFitter} parametrization, used for the determination of the HERAPDF set. It has been found that the combined inclusive HERA~I+II data can be described using NNLO theory with a significantly higher quality than HERAPDF2.0: the $\chi^2$ is reduced by more than 60 units, having used only four more parameters. Our result highlights a significant parametrization bias in the default \texttt{xFitter} parametrization at small $x$, which would lead to even more dramatic effects when used for higher energy colliders, where the small-$x$ region is more relevant. We also find that the inclusion of small-$x$ resummation leads to a further reduction by approximately 30 extra units in $\chi^2$. In this contribution, we review the results of the recent paper "A new simple PDF parametrization: improved description of the HERA data" (arXiv:1902.11125).