Step 1Place the yogurt in a large double cheesecloth and tie together like a pouch. Hang this over the kitchen sink and let it strain for about 2 hours. Or, strain the yogurt through a fine mesh sieve set over a bowl. The yogurt should be the consistency of sour cream. Place the yogurt in a bowl.
Step 2Grate the cucumber. Take a handful at a time and press the cucumber between the palms of your hands until most of the liquid is squeezed out. Add to the yogurt. Toss together with the garlic and olive oil, and season to taste with salt. Chill 1 hour and serve as an accompaniment to either of the souvlaki dishes.