A sensitive high-resolution sub-Doppler detecting spectrometer, based on noise-immune cavity-enhanced optical heterodyne molecular spectrometry (NICE-OHMS), for trace gas detection of species whose transitions have severe spectral overlap with abundant concomitant species is presented. It is designed around a NICE-OHMS instrumentation utilizing balanced detection that provides shot-noise limited Doppler-broadened (Db) detection. By synchronous dithering the positions of the two cavity mirrors, the effect of residual etalons between the cavity and other surfaces in the system could be reduced. An Allan deviation of the absorption coefficient of 2.2 × 10-13 cm-1 at 60 s, which, for the targeted transition in C2H2, corresponds to a 3σ detection sensitivity of 130 ppt, is demonstrated. It is shown that despite significant spectral interference from CO2 at the targeted transition, which precludes Db detection of C2H2, acetylene could be detected in exhaled breath of healthy smokers.