Put 1 ½ cups cooked wild rice and water in a saucepan, reserving ½ cup. Place over high heat, bring to a boil and reduce to a simmer. Cook until the rice is very soft and the water has evaporated. Drain. In a food processor fitted with a steel blade, puree the rice into a sticky dough. Place the dough in a medium bowl and work in the salt, sugar and remaining rice.
Scoop out ¼ cup dough for each patty and shape to ½ inch thick rounds. Heat the oil in a heavy skillet and brown the patties about 5-8 minutes per side until lightly browned. Transfer patties to a baking sheet and place in a warm oven until ready to serve.