Line a fine wire-mesh strainer with 3 layers of cheesecloth or 1 coffee filter. Place strainer over a bowl. Spoon yogurt into strainer. Cover yogurt with plastic wrap, and chill 2 hours.
Spoon yogurt into a bowl, discarding strained liquid. (Yogurt will be thick.) Stir in chopped cucumber and next 3 ingredients. Chill at least 1 hour. Garnish, if desired.