Put popped corn in a large bowl or metal dishpan; place in warm oven (225°).
Combine sugars, honey and water in 2-qt. heavy saucepan. Heat slowly, stirring until sugar is dissolved. Cook to firm ball stage (242°). Add butter and stir only enough to mix. Slowly pour the hot syrup over warm popped corn; mix thoroughly.
With buttered palms and fingers, shape immediately into balls slightly larger than a baseball, using as little pressure as possible.