  We introduce a weaker variant of the concept of three point property, which
is equivalent to a non-linear local connectivity condition introduced in [12],
sufficient to guarantee the extendability of a conformal map f from the unit
disk onto a domain to the entire plane as a homeomorphism of locally
exponentially integrable distortion. Sufficient conditions for extendability to
a homeomorphism of locally p-integrable distortion are also given.
