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In the last decade, battery manufacturers have significantly reduced the internal series resistance of many electrochemical energy storage devices. This reduction has drastically increased the power density available from these electrochemical cells and opened up a whole new set of applications that they can be used to power, such as compact pulsed power systems and electric vehicles. It has been shown previously that high-power lithium-ion battery cells, such as the Saft VL8V and GAIA 27-Ah battery, are capable of discharging currents at rates much higher than their rated C values for time scales on the order of tens of milliseconds. While these cells are capable of elevated rate discharge, recharge at an elevated rate is traditionally thought of as being catastrophic to the cell lifetime. In all applications, there is always a desire to recharge electrochemical energy storage devices at a faster rate. Previous research in this area has applied charge rates to batteries that are a few times the cell's rated C value in a steady-state application with findings that recharge time can be significantly reduced. The University of Texas at Arlington is conducting new research in this area. The aim of the research is to understand the charge rate limitations of electrochemical energy storage devices, such as lithium-ion batteries, supercapacitors, and lithium-ion capacitors, when the elevated charge is applied in a pulsed fashion. The effect that these types of elevated recharge rates have on the fundamental material properties inside the cells is being researched as well. This paper describes the rationale behind the experiments, the experimental setup developed, and the research progress made thus far.