  Let $D$ and $\Omega$ be Jordan domains with Dini's smooth boundaries and and
let $f:D\mapsto \Omega$ be a harmonic homeomorphism. The object of the paper is
to prove the following result: If $f$ is quasiconformal, then $f$ is Lipschitz.
This extends some recent results, where stronger assumptions on the boundary
are imposed, and somehow is optimal, since it coincides with the best condition
for Lipschitz behavior of conformal mappings in the plane and conformal
parametrization of minimal surfaces.
