In a large bowl, combine the water, salt and sugar, stirring to dissolve the salt. Using a paring knife or scissors, slit each shrimp down the back through the shell; remove the dark veins.
Add the shrimp to the brine, cover and refrigerate for 4 hours.
Light a grill.
Drain the shrimp and pat dry. Grill the shrimp over moderately high heat, turning once, until the shells are lightly charred and the shrimp are just cooked through, about 5 minutes.
