Sheet-crack cements and coextensive intrastratal folds and breccias occur in a stratigraphically controlled, meter-thick zone, near the base of Marinoan (635 Ma) cap dolostones in slope settings. We demonstrate that sheet-crack cements on the margins of the Congo and Kalahari cratons are localized at a turbidite-to-grainstone transition, which records a transient fall in relative sea-level, preceding the larger glacioeustatic transgression. Sheet-cracks opened vertically, implying that pore-fluid pressure exceeded lithostatic pressure. When the margin of an ice-sheet retreats from a coast, a net fall in sea-level occurs in the vicinity, because of the weakened gravitational attraction between the ice-sheet and the nearby ocean. Augmented by glacioisostatic adjustment (postglacial rebound), the early regional fall in relative sea-level can mask the simultaneous rise in global mean sea-level caused by the addition of meltwater. We propose that sheet-cracks and related structures in Marinoan cap dolostones manifest pore-fluid overpressures resulting from rapid sea-level falls in the vicinity of vanishing ice-sheets.