This article discusses the depth range which automultiscopic 3D (A3D) displays should reproduce for ensuring an adequate perceptual quality of substantially deep scenes. These displays usually need sufficient depth reconstruction capabilities covering the whole scene depth, but due to the inherent hardware restriction of these displays this is often difficult, particularly for showing deep scenes. Previous studies have addressed this limitation by introducing depth compression that contracts the scene depth into a smaller depth range by modifying the scene geometry, assuming that the scenes were represented as CG data. The previous results showed that reconstructing only a physical depth of 1 m is needed to show scenes with much deeper depth and without large perceptual quality degradation. However, reconstructing a depth of 1 m is still challenging for actual A3D displays. In this study, focusing on a personal viewing situation, we introduce a dynamic depth compression that combines viewpoint tracking with the previous approach and examines the extent to which scene depths can be compressed while keeping the original perceptual quality. Taking into account the viewer's viewpoint movements, which were considered a cause of unnaturalness in the previous approach, we performed an experiment with an A3D display simulator and found that a depth of just 10 cm was sufficient for showing deep scenes without inducing a feeling of unnaturalness. Next, we investigated whether the simulation results were valid even on a real A3D display and found that the dynamic approach induced better perceptual quality than the static one even on the real A3D display and that it had a depth enhancing effect without any hardware updates. These results suggest that providing a physical depth of 10 cm on personalized A3D displays is general enough for showing any deeper 3D scenes with appealing subjective quality.