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In this paper, we present a study to show that matching the dimensionality of interaction techniques with the dimensional demands of the task results in an interface that facilitates superior performance on interaction tasks without sacrificing performance on 2D tasks in favor of 3D tasks and vice versa. We describe the concept of dimensional congruence and how to identify the dimensional characteristics of a task so that appropriate interaction techniques can be applied. We constructed a prototypical application in a Virtual Environment Enclosure (VEE) using a hand-held device to show how this might be done in this type of apparatus. We then describe a study that evaluates both 2D and 3D tasks as performed using typical 2D and 3D interaction techniques. Results show that an appropriate mix of 2D and 3D interaction techniques is preferred over exclusive use of one or the other. The challenge lies not in selecting independent interaction techniques for specific tasks, but rather in constructing an overall interface that mixes 2D and 3D interactions appropriately.