Thaw the fish, if frozen. Rinse fish. Cut the fish into 4- or 6-serving-size pieces, if necessary. Measure thickness of the fish.
Combine flour, salt, and pepper. Coat fish with flour mixture.
Heat 2 tablespoons of olive oil in a large skillet over medium heat. Cook half of the fish for 4 to 6 minutes per 1/2-inch thickness of fish, or until the fish is golden brown and flakes easily with a fork. Turn the fish once halfway through cooking time.
Remove fish from skillet; keep warm. Add remaining olive oil to skillet. Cook the remaining fish as above; remove from skillet. Reduce heat.
Carefully add butter, capers, vinegar, and water to skillet. Cook and stir until butter just browns. Remove from heat. Stir in parsley. Spoon sauce over fish. Garnish with lemon wedges, if you like. Makes 4 to 6 servings.