  We show that for any dimension t>2(1+alpha K)/(1+K) there exists a compact
set E of dimension t and a function alpha-Holder continuous on the plane, which
is K-quasiregular only outside of E. To do this, we construct an explicit
K-quasiconformal mapping that gives, by one side, extremal dimension distortion
on a Cantor-type set, and by the other, more Holder continuity than the usual
1/K.
