  We apply a Gutzwiller-like variational technique to study Josephson
conduction across a quantum dot with an odd number of electrons connected to
two superconducting leads. Our method projects out all states on the dot but
the Kondo singlet and is valid when Kondo correlations are dominant and no
Andreev bound states localized at the dot are available for Kondo screening. In
these conditions superconducting pairing is a competing effect and the junction
is $\pi -$like, to optimize antiferromagnetic correlations on the dot. As the
superconducting gap increases, the Josephson current also increases, but its
phase dependence becomes strongly non sinusoidal.
