Quarter and seed 2 tangerines. From the third, cut a wedge; then, using a vegeta- ble peeler, cut a wide strip of zest from rest of fruit. Set wedge and zest aside.
Put quartered tangerines in a cocktail shaker and muddle thoroughly to break up fruit and release juice. Add rye, simple syrup, egg white, lemon juice, and orange bitters, then fill shaker with ice cubes. Shake vigorously about 20 seconds.
Strain into an old-fashioned glass and add 1 large ice cube. Bruise tangerine zest a bit with fingers to release oils, skewer with tangerine wedge, and set in drink.
*Clementines may also be sold as Cuties, Sweeties, Sunkist Delites, and Halos.
**Find simple syrup with cocktail supplies or make your own: Heat 1/4 cup each sugar and water, stirring, until sugar dissolves; let cool. Find pasteurized egg white at well- stocked grocery stores.