Battery management systems (BMS) require computationally simple but highly accurate models of the battery cells they are monitoring and controlling. Historically, empirical equivalent-circuit models have been used, but increasingly researchers are focusing their attention on physics-based models due to their greater predictive capabilities. These models are of high intrinsic computational complexity and so must undergo some kind of order-reduction process to make their use by a BMS feasible: we favor methods based on a transfer-function approximation to battery-cell dynamics. In prior works, transfer functions have been found from full-order PDE models via two assumptions: (1) a linearization assumption—which is a fundamental necessity in order to make transfer functions—and (2) an assumption made out of expedience that decouples the electrolyte-potential and electrolyte-concentration PDEs in order to render an approach to solve for the transfer functions from the PDEs. This paper shows how to eliminate the need for the second assumption, thus retaining the coupling between these two PDEs and improving overall model accuracy. Time-domain models created from these transfer functions are especially improved when simulating constant-current profiles since the electrolyte concentration gradient increases the coupling between the electrolyte-potential and electrolyte-concentration PDEs.