The potential of fiber-laser-based sub-Doppler noise-immune cavity-enhanced optical heterodyne molecular spectrometry for trace gas detection is scrutinized. The non-linear dependence of the on-resonance sub-Doppler dispersion signal on the intracavity pressure and power is investigated and the optimum conditions with respect to these are determined. The linearity of the signal strength with concentration is demonstrated and the dynamic range of the technique is discussed. Measurements were performed on C(2)H(2) at 1531 nm up to degrees of saturation of 100. The minimum detectable sub-Doppler optical phase shift was 5 x 10(-11) cm(-1) Hz(-1/2), corresponding to a partial pressure of C(2)H(2) of 1 x 10(-12) atm for an intracavity pressure of 20 mTorr, and a concentration of 10 ppb at 400 mTorr.