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Loudness is the quality of human perception that is most related to acoustic intensity and energy, however there is no agreed-upon way of integrating loudness over time for the prediction of noise-induced annoyance. Most noise metrics used today for aircraft certification and regulation employ the “Equal-Energy Hypothesis” (EEH) and sum the acoustical energy of one or more noise events over time to create a single metric value that represents the entire exposure. Using the EEH creates a natural tradeoff between the peak energy and the duration of a single noise event, the “hypothesis” being that this tradeoff optimally predicts annoyance in a wide variety of situations. This work proposes a strategy for integrating a loudness-like time series which is flexible in two ways: First, it includes a parameter b ∈ [0,1]. When b = 0, the metric will return the peak of the time series. At b = .5, the metric will behave in accordance with the EEH. At b = 1, the metric will penalize the duration of the sound more than the EEH would. Second, transformations are given so that the strategy can be computed from, or generate quantities in units analogous to, decibels (or phon), physical units (acoustic pressure/power), or perceptually-scaled units (sone). This approach is demonstrated on a dataset of annoyance responses to single events of UAV and road vehicle noise that is fit with an augmented linear regression. Analyses based on this integration of A-weighted level and the output of the “Zwicker” loudness model yield similar results: that subjects may have been slightly more sensitive to the durations of the events than the EEH would suppose, but that the EEH cannot be disproven using these data. The time-integrated metrics outperform both time-averaged and centile-based metrics.