The tug of relative sea level (RSL), set by climate and tectonics, is widely viewed as the most important boundary condition for the evolution of deltas. However, the range of amplitudes and periodicities of RSL cycles stored in deltaic stratigraphy remains unknown. Experimental results presented here suggest that extraction of RSL cycles from the physical stratigraphic record requires their magnitudes and periodicities to be greater than the spatial and temporal scales of the internal (autogenic) dynamics of deltas. These results predict stratigraphic storage of information pertaining to RSL cycles during icehouse Earth conditions. However, these thresholds commonly overlap with the magnitudes and periodicities of RSL cycles for major river deltas during greenhouse Earth conditions, suggesting stratigraphic signal shredding. This theory suggests quantitative limits on the range of paleo-RSL information that can be extracted from stratigraphy, which could aid the prediction of deltaic response to climate change.