We present a new one-dimensional parameterization of gravity drainage implemented in an all-new thermodynamic component of the Los Alamos Sea Ice Model (CICE), based on mushy layer theory. We solve a set of coupled, nonlinear equations for sea-ice temperature (enthalpy) and salinity using an implicit Jacobian-free Newton-Krylov method. Time resolved observations of gravity drainage show two modes of desalination during growth. Rapid drainage occurs in a thin region just above the ice/ocean interface while slower drainage occurs throughout the ice. Parameterizations are designed to represent each of these modes and work simultaneously. Near the interface, desalination occurs primarily via the fast drainage, while slow drainage continues to desalinate ice above the interface. The rapid desalination is convectively driven and is parameterized based on a consideration of flow driven upward within the mush and downward in chimneys, modified by the Rayleigh number. The slow desalination is represented as a simple relaxation of bulk salinity to a value based on a critical porosity for sea-ice permeability. It is shown that these parameterizations can adequately reproduce observational data from laboratory experiments and field measurements.