The performance of fiber-laser-based noise-immune cavity-enhanced optical heterodyne molecular spectrometry (NICE-OHMS) has been improved by elimination of the technical constraints that limited its first demonstration. Doppler-broadened detection of C(2)H(2) and CO(2) at ~1531 nm is demonstrated using a cavity with a finesse of 4800. Frequency and wavelength modulated detection at absorption and dispersion phase are compared and the optimum mode of detection is discussed. A minimum detectable absorption of 8 x 10-(11) cm(-1), which corresponds to a detection limit of 4.5 ppt (2 ppt.m) for C(2)H(2), was obtained for an acquisition time of 0.7 s by lineshape fitting. The linearity of the pressure dependence of the signal strengths is investigated for both C(2)H(2) and CO(2).