We study Koebe orderings of planar graphs: vertex orderings obtained bymodelling the graph as the intersection graph of pairwise internally-disjointdiscs in the plane, and ordering the vertices by non-increasing radii of theassociated discs. We prove that for every d∈N, any such orderinghas d-admissibility bounded by O(d/lnd) and weak d-coloring numberbounded by O(d4lnd). This in particular shows that the d-admissibilityof planar graphs is bounded by O(d/lnd), which asymptotically matches aknown lower bound due to Dvo\v{r}\'ak and Siebertz.<br