Lithium-ion battery models that estimate their energy content after a series of charge and discharge operations are essential in the optimal design, analysis, and operation of battery-based systems. We focus on the class of battery models that can be calibrated entirely from the batteries manufacturer-provided specifications (spec). Such models are simple to calibrate and are therefore widely used in practice. The best-known model in this category was proposed by Tremblay et al. in 2007. This model, however, has several shortcomings, including low fidelity at high C-rates, and the fact that it does not model the battery management system. We propose an alternative, called the Power-based Integrated model that is also completely spec-based, yet has much higher fidelity. We perform two types of validation, the first one uses the voltage profiles in the spec while the other is based on laboratory experiments. Both validations confirm that our model, which we have publicly released as a Simulink system block, has a mean absolute voltage error of less than 0.1 V across a wide range of C-rates.