Whitefish in caper-butter sauce

Credit for this recipe goes to Alton Brown, although I don't recall the precise “Good Eats” recipe it came from. This rewording is mine, so far as I know. (I have not compared it to the transcript.) It is important that the fish fillet be as even in thickness as possible. Note that by “whitefish”, I mean the market category and not members of the subfamily Coregoninae; I've never tried the latter.

1 lb whitefish fillet
1 tbl vegetable oil
1 tbl butter
  salt and pepper
  flour for dredging
  reserved pan liquids
1 tbl capers, drained and rinsed
1 tbl butter
1 lemon, juiced
  chopped parsley for garnish

To cook fish: Season fish and dredge in flour. Shake off any excess. Heat butter and oil in skillet to just below the smoke point. Carefully lay in fish fillets. Cook for two minutes on each side. Remove to warm plate.

To make sauce: Add butter to pan. Fry capers, moving pan rapidly, for 30 seconds. Remove from heat and add lemon juice.

To serve: Pour sauce over fish and garnish with parsley.