Filters from the Gammatone family are often used to model auditory signal processing, but the filter constant values used to mimic human hearing are largely set to values based on historical psychoacoustic data collected several decades ago. Here, we move away from this long-standing convention, and estimate filter constants using a range of more recent reported filter characteristics (such as quality factors and ratios between quality factors and peak group delay) within a characteristics-based framework that clarifies how filter behavior is related to the underlying constants. Using a sharp-filter approximation that captures shared peak-region behavior across certain classes of filters, we analyze the range of behaviors accessible when the full degrees of freedom of the filter are utilized rather than fixing the filter order or exponent to historically prescribed values. Filter behavior is characterized using magnitude-based and phase-based characteristics and their ratios, which reveal which characteristics are informative for constraining filter constants and which are only weakly constraining. We show that these insights and estimation methods extend to multiple realizable filter classes from the Gammatone family and apply them, together with recent physiological and psychoacoustic observations, to derive constraints on and estimates for filter constants for human auditory filters. More broadly, this framework supports the design of auditory filters with arbitrary characteristic-level specifications and enables systematic assessment of how variations in filter characteristics influence auditory models, perceptual findings, and technologies that rely on auditory filterbanks.