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Lens breathing in movie cameras is the change in the overall content of a scene while bringing subjects located at different depths into focus. This paper presents a method for minimizing lens breathing or changing angular field-of-view while maintaining perspective by moving only one lens group. To maintain perspective, the stop is placed in a fixed position where no elements between the scene and the stop can move, thus fixing the entrance pupil in one location relative to the object fields. The result is perspective invariance while refocusing the lens. Using paraxial optics, we solve for the moving group's position to focus on every object position and eliminate breathing between the minimum and maximum object distances. We investigate the solution space for optical systems with two positive groups or a positive and a negative group (i.e., retrofocus and telephoto systems). We explain how to apply this paraxial solution to existing systems to minimize breathing. The results for two systems altered using this method are presented. Breathing improved by two orders of magnitude in both cases, and performance specifications were still met when compared to the initial systems.