  We study the reduced dynamics of a spin (qubit) coupled to a spin-boson
environment in the case of pure dephasing. We derive formal exact expressions
which can be cast in terms of exact integro-differential master equations. We
present results for a SB environment with ohmic dissipation at finite
temperatures. For the special value of the ohmic damping strength K=1/2 the
reduced dynamics is found in analytic form. For K<<1 we discuss the possibility
of modulating the effect of the SB environment on the qubit. In particular we
study the effect of the crossover to a slow environment dynamics, which may be
triggered by changing both the temperature and the system-environment coupling.
