Juice the blood oranges.

In a pitcher, stir together the lime juice, sugar and ¾ cup water until the sugar has dissolved.

Add the tequila, Cointreau and blood orange juice.

Rub the rims of three 6-ounce martini glasses with the cut side of a lime half.

Spread coarse salt or sugar on a small plate and press the rims of the glasses until coated.

Fill a cocktail shaker about ¾ full of ice and measure in 1½ cups of the cocktail mix for 3 drinks. Cover and shake for about 15 seconds to thoroughly chill the mixture.

Strain into the glasses.

Garnish the glasses with a slice of blood orange and a slice of lime if desired.