1. Prepare an ice-water bath. Bring a large pot of water to a boil. Reduce heat to medium; poach shrimp until just cooked through, 1 1/2 to 2 minutes. Transfer shrimp to ice-water bath; let cool.

2. Drain shrimp, and peel; devein, and slice each in half. Toss shrimp with 1/2 cup lime juice in a nonreactive dish. Refrigerate, covered, stirring halfway through, for at least 2 hours. Drain.

3. Toss together shrimp, cucumber, mango, onion, jalapeno, cilantro, 2 tablespoons lime juice, 3/4 teaspoon salt, and a pinch of pepper. Refrigerate for 30 minutes. Stir in remaining tablespoon lime juice before serving.