Cut off the ends but don't peel them. Cut the cucumbers into paper thin slices.
In large bowl, mix cucumber slices with 2 teaspoons salt. Let sit at room temperature for 1 hour. Drain excess liquid from cucumbers.
In medium bowl, make dressing by whisking together the white wine vinegar, sugar, dill, white pepper, and 1 teaspoon salt. Pour vinegar dressing over the drained cucumbers and mix well, tossing to coat.
Cover salad with plastic wrap and refrigerate 3 hours before serving.
Don't skip the "salting" step. There's a reason for this. Salting the cucumbers draws out the liquid, keeping your salad from becoming diluted and less flavorful.