Place salt in a plastic bowl wide enough to fit the rim of a martini glass. Rub the rim of the glass with a lime wedge. Then dip the glass into the bowl of salt to coat the rim. Set glass aside.
To an ice-filled cocktail shaker, add tequila, Cointreau, orange juice, lime juice, and olive brine. Shake until thoroughly chilled. Pour into a martini glass, top off with Sprite, and garnish with jalapeño-stuffed olives.