We describe how current baseball physics models predict a class of towering pop ups in which the ball trajectory is steep enough to exceed the angle of repose, resulting in upward curvature. When optical interceptive control strategies like Optical Acceleration Cancellation (OAC) and Linear Optical Trajectory (LOT) are applied to such trajectories they produce systematic vacillations in running paths. We refer to these fly balls as Paradoxical Pop Ups because they behave fundamentally differently than typical near-parabolic fly balls. Paradoxical Pop Ups comprise a unique set of trajectories that can exhibit discrete cusps and loops near the apex, and tend to be more symmetric than typical. These trajectory abnormalities appear to misinform the typically robust optical control strategies used by fielders, which can lead to systematic lurching, especially when the pop up is headed to land near the fielder. It is useful for perception-action modelers to be aware of these deviant cases given that a number of research laboratories that study interception currently use near-parabolic models of ball trajectories in lieu of direct location measurements. In short, current perception-action research may benefit from more accurate physical modeling. In the case of fielders pursuing paradoxical pop ups, some of their dancing around can be well explained as a combination of bizarre trajectories and misguidance by the normally reliable optical control strategy, and is likely not due odd wind conditions, too much chew tobacco, or apparent fielder error. Behaviorally, even professional baseball players occasionally find it difficult to gracefully approach these seemingly routine pop-ups, and former Major League infielders confirm that their experiences agree with our predictions.