Cavity ringdown (CRD) absorption spectroscopy enables spectroscopic sensing of gases with a high sensitivity and accuracy. Instrumental improvements result in a new high-performance continuous-wave (cw) CRD spectrometer using a rapidly-swept cavity of simple design. It employs efficient data-acquisition procedures, high-reflectivity mirrors, a low-adsorption flow cell, and various compact fibre-optical components in a single-ended transmitter-receiver configuration suitable for remote sensing. Baseline noise levels in our latest cw-CRD experiments yield a competitive noise-equivalent absorption limit of ∼ 5×10-10 cm -1Hz-1/2, independent of whatever molecules are to be detected. Measurements in the near-infrared wavelength range of 1.51-1.56 μm yield sub-ppmv (i.e., ppbv or better) sensitivity in the gas phase for several representative molecules (notably CO2, CO, H2O, NH 3, C2H2, and other hydrocarbons). By measuring spectroscopic features in the 1.525 μm band of C2H2 gas, we realise detection limits of 19 nTorr (2.5×10-11 atm) of neat C2H2 (Doppler-limited at low pressure) and 0.37 ppbv of C2H2 in air (pressure-broadened at 1 atm). Our cw-CRD spectrometer is a high-performance sensor in a relatively simple, low-cost, compact instrument that is amenable to chemical analysis of trace gases in medicine, agriculture, industry, and the environment.