The classical Painlevé theorem tells us that sets of zero length are removable for bounded analytic functions, while (some) sets of positive length are not. For general $K$ -quasiregular mappings in planar domains, the corresponding critical dimension is ${2}/({K+1})$ . We show that when $K>1$ , unexpectedly one has improved removability. More precisely, we prove that sets $E$ of $\sigma$ -finite Hausdorff $({2}/({K+1}))$ -measure are removable for bounded $K$ -quasiregular mappings. On the other hand, $\dim(E) = {2}/({K+1})$ is not enough to guarantee this property.
¶ We also study absolute continuity properties of pullbacks of Hausdorff measures under $K$ -quasiconformal mappings: in particular, at the relevant dimensions $1$ and ${2}/({K+1})$ . For general Hausdorff measures ${\cal H}^t$ , $0 \lt t \lt 2$ , we reduce the absolute continuity properties to an open question on conformal mappings (see Conjecture 2.3)