The first ice formation in Arctic and Antarctic waters is often grease ice, a mixture of sea water and frazil-ice crystals. This grease ice solidifies as pancake ice, or a more solid sea-ice type (nilas), depending on ocean surface conditions like waves and turbulence, as well as heat fluxes. Grease ice thus produces a transition between open water and solid ice, gradually changing the heat fluxes and other open ocean properties. Some attempts have been made to model grease ice, and they all depend on the grease ice thickness parameterization. In fact all sea-ice models use a lower thickness limit on the solid sea ice, representing the transition from grease to solid ice. Here the existing but limited measurements of grease ice thickness are compared with different thickness parameterizations. The measurements are too few to exclude a linear dependence on wind speed, but scaling the wind drag and the back pressure from the grease layer, a quadratic relation is suggested. The relation is consistent with an increasing grease ice thickness towards a slower-moving solid boundary – often termed a grease (or frazil-ice) wedge. The new thickness parameterization is applied in detail on grease ice data from Storfjorden. In Storfjorden, tidal currents are strong enough to add significant drag force on the grease ice. For a ‘normal’ wind speed of 4 m s^–1 the tidal currents will likely double the grease ice thickness from 0.4 to 0.8 m.