I can't help but thinking of the Simpsons episode "Bart the Mother"
Principal Skinner: Well, I was wrong. The lizards are a godsend.
Lisa: But isn't that a bit short-sighted? What happens when we're overrun by lizards?
Principal Skinner: No problem. We simply unleash wave after wave of Chinese needle snakes. They'll wipe out the lizards.
Lisa: But aren't the snakes even worse?
Principal Skinner: Yes, but we're prepared for that. We've lined up a fabulous type of gorilla that thrives on snake meat.
Lisa: Then we're stuck with gorillas!
Principal Skinner: No, that's the beautiful part. When wintertime rolls around, the gorillas simply freeze to death.
Lisa: Hmm.
EDIT: Yes, I understand you are referring to keeping predators around, and not necessarily introducing new predators. But this is still what jumped in to my mind.
Principal Skinner: Well, I was wrong. The lizards are a godsend.
Lisa: But isn't that a bit short-sighted? What happens when we're overrun by lizards?
Principal Skinner: No problem. We simply unleash wave after wave of Chinese needle snakes. They'll wipe out the lizards.
Lisa: But aren't the snakes even worse?
Principal Skinner: Yes, but we're prepared for that. We've lined up a fabulous type of gorilla that thrives on snake meat.
Lisa: Then we're stuck with gorillas!
Principal Skinner: No, that's the beautiful part. When wintertime rolls around, the gorillas simply freeze to death.
Lisa: Hmm.
EDIT: Yes, I understand you are referring to keeping predators around, and not necessarily introducing new predators. But this is still what jumped in to my mind.