Among the existing measures of heart rate variability (HRV), the pNN50 statistics is one of the most commonly reported. However, it is only a single member of a much larger family of HRV measures -the pNNx statistics. In this research pNNx was further extended, combining it with the Lempel-Ziv complexity (LZ76) in a controlled neonatal stress framework. Forty healthy newborns were recorded undergoing two different types of stress stimuli -a routine heel stick blood sampling, and a dull heel pressure stimulation. Instead of relying on a single value, the entire spectrum from pNN1 to pNN100 was calculated, along with LZ76 derived from binarized sequences for each NN. The results of this study show a downward shift of the pNNx curves when newborns are stressed, with reduced LZ76 complexity when stressed.When ROC curves were utilized for the pNNx statistics and LZ76, however, the highest AUC values were observed when both measures were combined, with the highest AUC values of 0.88 (0.80-0.94) and 0.85 (0.74-0.91) for discriminating resting states from stress phases.Combining the widely used pNNx statistics with LZ76 extends the existing HRV toolbox, and shows a promising application in recognizing acute neonatal stress.