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 much less than 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.