The design of predictive, electrochemical, Li-ion battery models and the use of model-order reduction techniques to extract low-order models enables researchers to address problems related to model-based control, estimation, aging, and life-cycle prediction. This paper presents a novel approach to the design and parametrization of a reduced-order model characterizing the dynamic voltage response of a Li-ion cell. The model is based on the assumption of uniform active material utilization and includes prediction of the ionic concentration and potential dynamics in the liquid phase, which significantly affects the voltage response for high currents. A model-order reduction procedure based on the Pade approximation method is used to reduce the partial differential equation model to a low-order system of ordinary differential equations. Systematic methods are proposed to identify the electrochemical parameters that govern power and capacity prediction, as well as their temperature dependence. The procedure is based on carefully designed experiments that isolate the influence of small groups of parameters on the voltage output, utilizing complete cell data for model identification almost entirely in place of half-cell characterization. Finally, an extensive validation with experimental data illustrates the ability of the model to accurately predict the cell voltage.