Cut off the stems of the artichokes. If using Argentinian-style artichokes, use kitchen scissors to trim the tips of the leaves to avoid getting pricked. Gently open the leaves and wash the artichokes. Spanish artichokes have rounded tips and don't need trimming.
Fill a pot with water and bring to a boil. You can add salt to the water if you like, but I prefer not to so I can drink the liquid once it's cooled.

Once the water is boiling, add the artichokes and place a plate on top to keep them submerged. The artichokes are done when a leaf pulls out easily. If you overcook them, the leaves will fall off.
Remove the artichokes from the water and let them cool.

Remove the center of the artichokes and use a small spoon to scoop out the fuzzy choke from the base. Mix the small shrimp with the onion, celery, mayonnaise, salt, and pepper to taste.

Stuff the artichokes with the shrimp salad.
Serve the stuffed artichokes on a bed of lettuce with tomatoes, cucumbers, and olives, dressed with lemon juice, olive oil, and salt.
Place the medium shrimp on top of the artichokes.
Arrange the center leaves on the side.

Serve the artichokes with the dipping sauce in small bowls for dipping the artichoke leaves.