Decoherence effects associated to the damping of a tunneling two-level syst
em are shown to dominate the tunneling probability at short times in strong
-coupling regimes in the context of a soluble model. A general decompositio
n of tunneling rates in dissipative and unitary parts are implemented. Mast
er equation treatments fail to describe the model system correctly when mor
e than a single relaxation time is involved.