A refrigerator includes an ice compartment region disposed in at least one of a fresh food compartment or a freezer compartment; an ice maker disposed in the ice compartment region and configured to make ice pieces; and an ice bucket assembly configured to store the ice pieces made by the ice maker. The ice bucket assembly includes a mechanism for producing nugget ice from the ice pieces made by the ice maker and stored in the ice bucket assembly, the nugget ice being smaller in size as compared to the ice pieces made by the ice maker and stored in the ice bucket assembly.