Line a sieve with either a double thickness of dampened cheesecloth or linen tea towel. Spoon in yogurt and set the sieve over a bowl. You may also strain it through a coffee filter. Refrigerate for two to three hours or until yogurt is about half its volume, nicely thick and creamy. Shred or cut cucumber into julienne strips. Place in a colander in sink or over a bowl, sprinkle generously with salt, mix well and let drain for at least 30 minutes, preferably an hour. Rinse and gently pat dry. Press the garlic into a bowl and, using a fork, mash it with a little bit salt. Add the thickened yogurt, cucumber, lemon juice, olive oil, and if desired, the pepper and mint. Mix well. Serve or refrigerate up to two days so flavors will mingle. Stir again before serving and sprinkle with additional minced mint leaves if desired.