A wavelet-neural network signal processing method has demonstrated approximately 10-fold improvement over traditional signal processing methods for the detection limit of various nitrogen and phosphorus compounds from the output of a thermionic detector attached to a gas chromatograph. A blind test was conducted to validate the lower detection limit. All 14 of the compound spikes were detected when above the estimated threshold, including all 3 within a factor of 2 above the threshold. In addition, two of six spikes were detected at levels of half the concentration of the nominal threshold. Another two of the six would have been detected correctly if we had allowed human intervention to examine the processed data. One apparent false positive in five nulls was traced to a solvent impurity, whose presence was subsequently identified by analyzing a solvent aliquot evaporated to 1% residual volume, while the other four nulls were properly classified. We view this signal processing method as broadly applicable in analytical chemistry, and we advocate that advanced signal processing methods should be applied as directly as possible to the raw detector output so that less discriminating preprocessing and postprocessing does not throw away valuable signal.