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Understanding the dynamics of Fourier domain mode-locked (FDML) lasers is crucial for determining physical coherence limits, and for finding new superior methods for experimental realization. In addition, the rich interplay of linear and nonlinear effects in a laser ring system is of great theoretical interest. Here we investigate the dynamics of a highly dispersion-compensated setup, where over a bandwidth of more than 100 nm, a highly coherent output with nearly shot-noise-limited intensity fluctuations was experimentally demonstrated. This output is called the sweet-spot. We show by numerical simulation that a finite amount of residual dispersion in the fiber delay cavity of FDML lasers can be compensated by the group delay dispersion in the swept bandpass filter, such that the intensity trace exhibits no dips or high-frequency distortions, which are the main source of noise in the laser. In the same way, a small detuning from the ideal sweep filter frequency can be tolerated. Furthermore, we find that the filter's group delay dispersion improves the coherence properties of the laser, and acts as a self-stabilizing element in the cavity. Our theoretical model is validated against experimental data, showing that all relevant physical effects for the sweet-spot operating regime are included.