A cavity-enhanced absorption spectroscopy instrument has an optical cavity with two or more cavity mirrors, one mirror of which having a hole or other aperture for injecting a light beam, and the same or another mirror of which being partially transmissive to allow exit of light to a detector. A spherical-spherical configuration with at least one astigmatic mirror or a spherical-cylindrical configuration where the spherical mirror could also be astigmatic prevents a reentrant condition wherein the injected beam would prematurely exit the cavity through the aperture. This combination substantially increases the number of passes of the injected beam through a sample volume for sensitive detection of chemical species even in less than ideal conditions including low power laser or LED sources, poor mirror reflectivity or detector noise at the wavelengths of interest, or cavity alignment issues such as vibration or temperature and pressure changes.