An incoherent broad-band cavity-enhanced absorption (IBB-CEA) set-up was used in combination with a Fourier-transform (FT) spectrometer in order to explore the potential of this technique for high-resolution molecular spectroscopy in the near-infrared region. Absorption spectra of overtone bands of CO2, OCS, and HD18O were measured between 5800 and 7000 cm(-1) using a small sampling volume (1100 cm3, based on a 90 cm cavity length). The quality of the spectra in this study is comparable to that obtained with Fourier transform spectrometers employing standard multi-pass reflection cells, which require substantially larger sampling volumes. High-resolution methods such as FT-IBB-CEAS also provide an elegant way to determine effective mirror reflectivities (R(eff), i.e. a measure of the inherent overall cavity loss) by using a calibration gas with well-known line strengths. For narrow absorption features and non-congested spectra this approach does not even require a zero-absorption measurement with the empty cavity. Absolute cross-sections or line strengths of a target species can also be determined in one single measurement, if gas mixtures with known partial pressures are used. This feature of FT-IBB-CEAS reduces systematic errors significantly; it is illustrated based on CO2 as calibration gas.