Preheat the oven to 400F. Prepare 4 large sheets of parchment paper, about the size of a baking sheet.

To assemble the packets, layer a mound of potatoes in the center of 1 piece of parchment. Drizzle it with oil, and sprinkle with salt and pepper. Top with a piece of fish. Top the fish with several lemon slices, a bit more oil and salt, and 2 tablespoons white wine. Roll the edges of the parchment paper tightly to form a half-moon shaped packet. Repeat with the other 3 pieces of fish.

Bake the packets for 15 - 20 minutes until fish is cooked through and flaky. Remove gently from the packets and slide the fish, potatoes, and any juices onto plates. Serve topped with fresh dill and capers.