Bubble sort, but sloshing both directions each pass.
Bubble sort that reverses direction each pass — left-to-right to bubble the maximum up, then right-to-left to sink the minimum down. Small "turtle" values trapped near the back move toward the front twice as fast as in plain bubble sort.
Mostly-sorted data with a handful of out-of-place elements near either end. The bidirectional sweep catches both sides in a single round-trip, so one full cycle often finishes the job.
Any workload a real library sort could handle. Still O(n²) on average — cocktail only trims the constant, not the order of growth.