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Biophysical models describing complex cellular phenomena typically include systems of nonlinear differential equations with many free parameters. While experimental measurements can fix some parameters, those describing internal cellular processes frequently remain inaccessible. Hence, a proliferation of free parameters risks overfitting the data, limiting the model's predictive power. In this study, we develop systematic methods, applying statistical analysis and dynamical-systems theory, to reduce parameter count in a biophysical model. We demonstrate our techniques on a five-variable computational model designed to describe active, mechanical motility of auditory hair cells. Specifically, we use two statistical measures, the total-effect and PAWN indices, to rank each free parameter by its influence on selected, core properties of the model. With the resulting ranking, we fix most of the less influential parameters, yielding a five-parameter model with refined predictive power. We validate the theoretical model with experimental recordings of active hair-bundle motility, specifically by using Akaike and Bayesian information criteria after obtaining maximum-likelihood fits. As a result, we determine the system's most influential parameters, which illuminate the key biophysical elements of the cell's overall features. Even though we demonstrate with a concrete example, our techniques provide a general framework, applicable to other biophysical systems. Published by the American Physical Society2024