Energy is a critical concept in physics problem-solving, but is often a major source of confusion for students if the presentation is not carefully crafted by the instructor or the textbook. A common approach to problems involving deformable or rotating systems that has been discussed in the literature is to employ the work-kinetic energy theorem together with a "pseudowork-kinetic energy theorem" or a "center-of-mass equation." This article discusses an alternative approach that employs neither of these equations and allows students a more global and less confusing approach to such problems. The approach is demonstrated for three sample situations from the literature. [For Part IV, see EJ860240.]