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Snap the woody ends off the asparagus, and discard. Cut the tomatoes in half, spoon out and discard the seeds. Finely slice the tomato flesh, then cut into small dice. Set both asparagus and tomatoes aside.
Heat the 1 tbsp olive oil in a large frying pan. Season the fish with salt and pepper, and cook skin-side down over medium heat for about 3-4 minutes, gently pressing, until skin is crisped and golden. Turn and cook the other side for 3-4 minutes, depending on the thickness, until cooked.
Meanwhile, cook the asparagus in simmering salted water for 3-4 minutes. Drain well. For the dressing, gently warm the 3 tbsp olive oil in a small saucepan with the tomatoes, olives, capers and parsley leaves. Toss the asparagus in a little of the dressing. Arrange the asparagus on each of four warmed dinner plates, top with the fish, and spoon the warm tomato dressing around the fish.