When dividing a large system into a subsystem and a bath, one sometimes needs to include multiple nuclear coordinates in the subsystem in order to treat the remaining bath modes by Markovian relaxation theory (which assumes fast bath relaxation). This paper examines the effects of Redfield relaxation on the time-resolved fluorescence signal and on the loss of energy from a three-mode system. Simulations are compared for system coordinates coupled to the same bath mode and to independent bath modes, for coupling linear and quadratic in the system coordinates, and for different temperatures. To make these comparisons meaningful, a criterion is proposed for normalization of the coupling strengths in the different cases. The fluorescence Stokes shift and the system energy are shown to be sensitive to different relaxation processes. The coupling of multiple system coordinates to the same bath mode results in a wide range of relaxation rates. Simple descriptions in terms of individual population relaxation and coherence dephasing rates are inadequate due to sequential processes and to coupling between populations and coherences. These results have implications not only for Redfield treatments but also for other relaxation theories such as the Brownian oscillator model.