In a blender or food processor, combine berries, sugar, vanilla, and yogurt; whirl until mixture is smooth and sugar is dissolved.
If desired, press mixture through a fine sieve to remove seeds; discard seeds.
Pour mixture into frozen container of a cylinder ice cream freezer and freeze according to manufacturer's directions until desired consistency is achieved.
For soft-frozen yogurt, freeze for 15 to 30 minutes; remove lid and blade, then serve.
For firmer texture, remove blade; then replace lid and let stand in outer case for 20 to 30 more minutes.