Leave it alone.
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Char a whole fish on each side, then move it to the cool side of the grill, put the top down, and let it cook through. Set fillets skin-side down. When the edges curl and the flesh is opaque, move them over. Don't flip them. "Good grilled fish should have charred skin," Pelaccio says. "Don't worry you'll burn the fish. You'll hear it, watch it seize up, and think, 'I'm fucking up my fish.' Just wait a minute. Get a drink. Chill out."