Place fillets in a large skillet; add onion, celery, carrots, and seasonings. Add water to cover, and bring to a boil. Reduce heat; cover, and simmer 8 minutes or until fish flakes easily when tested with a fork.
Remove fish and vegetables to individual serving plates. Serve immediately.
Note: This recipe yields 4 cups coarsely chopped bluefish for use in a salad, if desired.