  In this article we explore a modification in the problem of controlling the
rotation of a two level quantum system from an initial state to a final state
in minimum time. Specifically we consider the case where the qubit is being
weakly monitored -- albeit with an assumption that both the measurement
strength as well as the angular velocity are assumed to be control signals.
This modification alters the dynamics significantly and enables the
exploitation of the measurement backaction to assist in achieving the control
objective. The proposed method yields a significant speedup in achieving the
desired state transfer compared to previous approaches. These results are
demonstrated via numerical solutions for an example problem on a single qubit.
