  We introduce a relaxed version of the metric definition of quasiconformality
that is natural also for mappings of low regularity, including
$W_{\mathrm{loc}}^{1,1}(\mathbb{R}^n;\mathbb{R}^n)$-mappings. Then we show on
the plane that this relaxed definition can be used to prove Sobolev regularity,
and that these ``finely quasiconformal'' mappings are in fact quasiconformal.
