Grate the cucumber and place it in a fine strainer over a bowl. Salt the cucumber and allow it to drain until most of the juices come out, approximately 10 minutes. Squeeze out the last bit of juices and transfer to paper towels to pat dry.
In a medium bowl, combine the cucumber, yogurt, white wine vinegar, garlic, mint and dill. Refrigerate to allow the flavors to meld, at least 1 hour. Season with salt and pepper before serving.