We describe and employ a recently developed polaron master equation model to study the fluorescence spectra of a coherently driven quantum dot (QD) placed within a high-Q semiconductor microcavity (with Q the quality factor). We investigate phonon-induced damping in a regime where many cavity photons are required, and we also compare the resonance fluorescence spectra obtained using an effective phonon master equation in Lindblad form where simple analytical expressions are identified for various phonon-induced scattering rates. We consider two separate continuous-wave pumping scenarios, where either the system is driven through exciton pumping or the system is driven via the cavity. The cavity-QED (quantum electrodynamics) system is pumped sufficiently strongly such that the low-energy sideband of the Mollow triplet is tuned across the cavity mode resonance which is negatively detuned from the QD. For comparison, we also consider the case where the QD-cavity detuning is large enough such that the Mollow triplets do not spectrally overlap with the cavity mode. We find that the full width at half maximum (FWHM) of the high-energy Mollow sideband shows a pronounced nonlinear dependence on the pump intensity when the low-energy component of the triplet overlaps with the cavity mode (or vice versa), and can even be reduced with increased pumping. However, the FWHM depends linearly on the pump intensity when the Mollow triplets are far from the cavity resonance. We observe similar fluorescence spectra for both the exciton-driven system and the cavity-driven system. (C) 2012 Elsevier B.V. All rights reserved.