We study the efficiency of exciton transport as a function of the typical reorganization time scale of the environment using the hierarchy of equations of motion. As a model system, we choose the Fenna-Matthews-Olson (FMO) complex. An environment in which the dynamics is not much faster than the system leads to prolonged quantum coherent transport, even at room temperature. We find that this does not make the transport process more efficient for standard FMO parameters, but does increase the efficiency in the case when exciton decay competes with trapping at the reaction center. We furthermore find that initial correlations do not influence population oscillations.