A thermodynamic sea ice model numerically structured to take time steps on the order of a week is found to be sensitive to time step size when new ice formed on open ocean is assumed to cover the ice-free area. This sensitivity is caused by the extrapolation of initial ice growth rates on open ocean, which can be very high, over the length of the time step. The sensitivity to time step size is tremendously reduced when the parameterization for the formation of new ice is altered so that the new ice thickness is specified. However, the sensitivity continues during the winter, when the area of open ocean is small because the volume of ice formed over the time step is more than enough to fill the open area at the specified thickness. Therefore ice thickness during the winter is again determined by time step size. Suggestions are made on how the sea ice model's sensitivity to time step size can be further reduced without sacrificing computational efficiency.