Make the brine. Add the water, white wine vinegar, sugar, and salt to a small saucepan. Heat over medium heat until the sugar and salt have dissolved.
Prepare the cucumbers. Cut the baby cucumbers lengthwise in 4, in half, or into slices (according to your personal preference).
Fill the jar. Add the cucumbers to a 16-ounces (500 ml) glass jar. Make sure they are tightly fitted and don't stick out from the jar (if they do, cut off the tops).
Pickle. Pour the warm vinegar brine on top and leave 0.5 inches (1,3 cm) head space at the top. Add in the dill, peppercorns, and mustard seeds. Give it a good stir. Make sure the cucumbers are completely submerged and close with a lid. Let it come to room temperature.
Cool and store. Place in the refrigerator overnight or for at least 20 minutes before serving.
Notes
White wine vinegar vs distilled white vinegar: White wine vinegar is milder, fruiter, and less pungent than white vinegar. If you want to substitute it you can use ⅓ cup white vinegar + ⅓ cup apple cider vinegar OR use ⅔ cup white vinegar but add an extra tablespoon of sugar.