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A novel eye-tracked measure of pupil diameter oscillation is derived as an indicator of cognitive load. The new metric, termed the Low/High Index of Pupillary Activity (LHIPA), is able to discriminate cognitive load (vis-à-vis task difficulty) in several experiments where the Index of Pupillary Activity fails to do so. Rationale for the LHIPA is tied to the functioning of the human autonomic nervous system yielding a hybrid measure based on the ratio of Low/High frequencies of pupil oscillation. The paper’s contribution is twofold. First, full documentation is provided for the calculation of the LHIPA. As with the IPA, it is possible for researchers to apply this metric to their own experiments where a measure of cognitive load is of interest. Second, robustness of the LHIPA is shown in analysis of three experiments, a restrictive fixed-gaze number counting task, a less restrictive fixed-gaze n-back task, and an applied eye-typing task.