We study the control problem for a general (finite dimensional) quantum system interacting with a bath. In the Hamiltonian formulation, the overall (system+environment) system varies on a Hilbert space which is the tensor product of the system and environment Hilbert spaces. We use sensitivity functions as a tool to compare the control laws and trajectories in this formulation. We treat the example of a spin 1/2 particle in a spin bath in detail. For this system, using optimal control theory and first order sensitivity as the cost, we explicitly derive the minimum decoherence controls.