Reserve 4 raspberries for garnish. Place the remaining berries in a large cocktail shaker or mixing glass. Add the lime juice. Muddle until the berries are completely smashed.

Set a small or hand-held mesh colander over a volume measuring cup. Pour the contents of the cocktail shaker in the colander and press with the muddler to extract the juice. If your colander is small, you may need to work in batches. Discard the seeds and pulp. You should end up with 4 ounces of thick juice.

Rinse any remnants of seeds from the cocktail shaker and add the raspberry-lime juice back to the shaker. Pour in the tequila and Cointreau. Add a ½ cup of ice. Shake or stir for 30 seconds until well chilled.

Rim two 10-to-12-ounce tall cocktail glasses with salt. Fill each with crushed ice. Strain an equal amount of the cocktail into each glass. Garnish each with two raspberries and a lime slice and serve.