Prepare an ice-water bath. Place eggs in a medium saucepan, and add cold water to cover by 1 inch. Bring to a boil. Cover, and remove from heat. Let stand for 13 minutes. Drain, and transfer eggs to ice-water bath; let stand until cool.
Peel eggs, and cut in half lengthwise. Transfer 3 yolks to a medium bowl, and mash with a fork until smooth; reserve remaining yolks for another use. Stir in yogurt, mustard, pepper, chopped dill, capers, and cucumber. Spoon filling into egg whites. Refrigerate until set, about 15 minutes or up to 1 hour. Garnish with dill sprigs just before serving.