Grate the cucumber on the coarse side of a grater. Place in a sieve, sprinkle with a little salt and leave to drain for 30 minutes.
Squeeze the excess water from the cucumber then stir into the yogurt. Add the garlic to taste then whisk in the oil and mint. Add a little red wine vinegar at a time, tasting in between each addition, to achieve a rounded sharpness against the creamy yogurt.
Season and refrigerate for at least 1 hour.