  Josephson tunnel junctions with the strong ferromagnetic alloy
$\Fe_{0.75}\Co_{0.25}$ as the barrier material were studied. The junctions were
prepared with high quality down to a thickness range of a few monolayers of
Fe-Co. An oscillation length of $\xi_{F2}\approx 0.79\:{\rm {nm}}$ between 0
and $\pi$-Josephson phase coupling and a very short decay length
$\xi_{F1}\approx 0.22\:{\rm {nm}}$ for the amplitude of the superconducting
pair wave function in the Fe-Co layer were determined. The rapid damping of the
pair wave function inside the Fe-Co layer is caused by the strong ferromagnetic
exchange field and additional magnetic pair breaking scattering. Josephson
junctions with Fe-Co barriers show a significantly increased tendency towards
magnetic remanence and flux trapping for larger thicknesses $d_{F}$.
