  The loss of coherence of quantum oscillations is of fundamental interest as
well as of practical importance in quantum computing. In solid-state
experiments the oscillations show, next to the familiar exponential decay on
time scales $T_{1/2}$, an overall loss of amplitude. We solve the spin-Boson
for a large class of initial conditions without the Markov approximation at the
pure dephasing point. It is shown that a loss of visibility occurs in the form
of a fast initial drop for factorized initial conditions and an overall
reduction for entangled initial conditions. This loss of amplitude is distict
from $T_2$-decoherence with the difference being most drastic for environments
with real or pseudo-gaps. This result is explained by bandwith effects in
quantum noise as well as in terms of higher-order phase-breaking processes. For
several experiments, such gapped environments are identified. We confirm that
this physics is valid beyond the pure dephasing point.
