Heat 2 tablespoons oil in a 12-inch heavy skillet over moderately high heat until hot but not smoking, then sauté onion, stirring frequently, until golden, about 6 minutes. Stir in water and 1/4 teaspoon pepper and cook, stirring, until onion is softened, about 1 minute. Stir in butter until melted, then stir in capers and lemon juice. Remove from heat and keep warm, covered.

Preheat broiler.

Pat fish dry, then brush all over with remaining tablespoon oil and sprinkle with salt and remaining 1/4 teaspoon pepper. Put fillets on rack of a broiler pan and broil about 5 inches from heat until just cooked through, 6 to 8 minutes.

Serve fish topped with onion, lemon, caper mixture and sprinkle with parsley.