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The Nondimensional Tire Model is based on the idea of data compression to load-independent curves. Through the use of appropriate transforms, tire data can be manipulated such that, when plotted in nondimensional coordinates, all data falls on a single curve. This leads to a highly efficient and mathematically consistent tire model. In the past, data for slip angle and slip ratio has been averaged across positive and negative values for use with the transforms. In this paper, techniques to handle tire asymmetries in lateral and longitudinal force are presented. This is an important advance, since in passenger cars driving/braking data is almost always asymmetric and, depending on tire construction, lateral force data may follow likewise. In addition, this paper is the first to explore the inclusion of inflation pressure as an operating variable in the Nondimensional Tire Theory.