  We show that a homeomorphism of Euclidean space is quasiconformal if and only
if at each point there exists a sequence of uncentered open sets with bounded
eccentricity shrinking to that point whose images also have bounded
eccentricity. This generalizes the metric definition of quasiconformality of
Gehring that uses balls instead. We also study exceptional sets for this
definition, in connection with sets that are negligible for extremal distances.
We introduce the class of CNED sets, generalizing the classical notion of NED
sets studied by Ahlfors--Beurling. A set $A$ is CNED if the conformal modulus
of a curve family is not affected when one restricts to the subfamily
intersecting the set $A$ at countably many points. We show as our main theorem
that CNED sets are exceptional for the definition of quasiconformality.
