Tip the yoghurt into a colander lined with a clean piece of muslin. Sit the colander in a bowl and leave in a cool place to drain for a few hours. Discard the liquid and tip the yoghurt into a clean mixing bowl.
Peel the cucumber and cut it in half lengthways. Use a teaspoon to remove the seeds, leaving a hollow centre. With a sharp knife, cut fine slices on the diagonal, like half- moons. Place these in a colander to drain away excess liquid (15-20 minutes).
Add the cucumber, mint, olive oil and garlic to the yogurt, season to taste. Fold in gently but throughly, then taste and adjust the seasonings to your liking.