Peel, devein, and cook the raw shrimp (if using): If you have pre-cooked, peeled and deveined shrimp you can skip to the next step. If you are working with raw shrimp, peel and devein them. If you have a little extra time and want your shrimp to be extra good, put the shells in 6 cups of cool salted water, bring to a boil, then strain the shell stock into a separate pot and cook the shrimp in that liquid. If you want to skip that step, just bring a medium pot salted water to a boil (a tablespoon salt for 2 quarts of water), add the shrimp, and cook for 2-3 minutes, until just cooked through. Reserve a cup of the cooking water and chill.

Cut half of the cooked shrimp into chunks: Cut half of the shrimp into large chunks, leaving the other half whole for a more attractive presentation.

Toss the shrimp with other ingredients, chill: Put the chopped shrimp in a bowl with the chopped onions, cucumber, celery, jalapeño, tomatoes, ketchup, cilantro, lime juice, and hot sauce. Gently stir to combine. Chill.

Add some cooled shrimp cooking water: Once the cooking water has cooled at least to room temperature, add a little at a time to the shrimp cocktail, until the shrimp cocktail is the consistency you want (use clam stock or lightly salted water—a third of a teaspoon of salt dissolved into a cup of water—if you are starting with already cooked and peeled shrimp).

Stir in the salt, hot sauce, avocado: To serve, add salt and more hot sauce to taste and gently mix in the chopped avocados. Dip the whole shrimp in the cocktail and arrange them on top. Serve in parfait glasses or in small bowls with tortilla chips on the side.