By the time that the Breen appeared on screen in Indiscretion, during the fourth season of Deep Space Nine, their status as an in-joke was confirmed. Their organic technology was mentioned in Scorpion, Part I.
Their nursery rhymes were a source of interest in For the Uniform. Their privateers were a threat dealt with off-screen in To the Death. Their athletes were discussed in Interface.
The Breen would pop up time and again in dialogue, sketching out a bizarre culture.
