Place a saucepan filled two-thirds with water over high heat. Cut potatoes into 1-inch pieces. Add potatoes to pan; cover and bring to a boil. Reduce heat to medium-high; cook 5 minutes or until tender. Drain.
Combine cucumber, sour cream, yogurt, dill, salt, and pepper in a large bowl. Add drained potatoes to cucumber mixture, and toss gently to coat.