A major goal of understanding Neoproterozoic glaciations and determining their effect on the evolution of life and Earth's atmosphere is establishing whether and how much open ocean there was during them. Geological evidence tells us that continental ice sheets had to flow into the ocean near the equator during these glaciations. Here we drive the Parallel Ice Sheet Model with output from four simulations of the ECHAM5/Max Planck Institute Ocean Model atmosphere-ocean general circulation model with successively narrower open ocean regions. We find that extensive equatorial ice sheets form on marine margins if sea ice extends to within about 20° latitude of the equator or less (Jormungand-like and hard snowball states), but do not form if there is more open ocean than this. Given uncertainty in topographical reconstruction and ice sheet ablation parameterizations, we perform extensive sensitivity tests to confirm the robustness of our main conclusions. Key Points Low-elevation eq. ice sheets form if sea ice extends to 20 degrees latitude This limits the amount of open ocean possible in Neoproterozoic glaciations This result is robust to large parameter variations ©2013. American Geophysical Union. All Rights Reserved.