Asymmetric media might be interesting for a very hierarchical species, where the ascending communication is actually in a different medium than the descending communication. I'm going to suggest a transmission method where the regent communicates using near-field sound fields, and the minions respond with interpretive dance within that sound field. You might think of it like the bee waggle dance, only on a dance floor with a DJ changing the tune while you dance.
Picture a species whose rulers have several mouths (or other noise making sources) and sufficient control over them to start setting up nulls in the soundscape in front of them, communicating not just with sound but sound fields. They communicate with the masses by sweeping these nulls around by varying the phase of each of their sound making organs. The workers are expected to dance around, keeping themselves in sync with these nulls. The message itself is encoded in the directions the nulls are swept. This communication mechanism is very secure because, unlike typical vocal communication, it depends heavily on near field communication that is simply not detectable at longer distances. You may be able to hear the strange screeching song of the regent, but the far field of the song itself contains none of the information content.
I suggest this for a hierarchical species because there's a few neat quirks that show up. First off, there's a neat little feedback loop that lets the masses communicate back. If a minion is not right smack on the null (and, in fact, potentially having to predict ahead where the regent will move it next), the regent has fewer options to communicate, but the messages are easy to understand because the regent is basically shouting as their voice drags the minion this way or that (obviously failure to follow the voice is grounds for execution). However, if the minion gets good at staying in the null, there's room for a bit of choice. Obviously the regent cannot expect a minion to perfectly predict the regent's will before the sounds reach it, but the regent can observe how the minion positions themselves and gain insight into what the minion is thinking. In fact, this forms a 2 way communication remarkably similar to that of a human dance. The regent has complete control over where the dance will go, but it is the minion that adds the spice to the conversation in the form of its sways and shimmies as it communes with it master. This, of course, reinforces the hierarchy. The better you are in tune with the regent, the more you are capable of saying within the language. Sergeants and Lieutenants don't get promoted into rank as much as they simply demonstrate that they have the commune's interest in mind with their dance, so are permitted to say more. Rebellious individuals find themselves in fields of sound which have less room for interpretive dance (and in fact, the worst offenders simply cannot speak at all, for without the regent's sound field to dance in, they literally have no way of speaking).
Inter tribal combat of this species can follow the lines Joe Bloggs suggested: smash. The two reagents begin generated competing sound fields and the minions all dance about (potentially with knives and other weapons) like they were salt granules on a Chlandi plate. Combat ends when one regent can no longer produce a meaningful sound field. Interestingly, this sort of warfare would not be wasteful. Any minions which a regent could trap within their own sound fields as POWs immediately become minions in their own army, by the mere fact that they are dancing to the reagent's tune. Rather than killing a weak regent, opposing rulers might simply siphon off their minions with superior control of the sound fields around them.
Also interesting is that it permits an opening for a promotion to regent. Once in a rare while, we get an opportunity to glimpse the dance of a lifetime. A minion whose dance has become so powerful that they are less of a minion and more of a suitor is in an intriguing position. Consider for a moment, the special case of an alien race with this provocative method of communication where even the minions have the organs to emit sound fields, but only regents are allowed to use them, causing atrophy in the minions. However, the skillset required to dance within the nulls is also the same skillset needed to learn how to practice using their voice without anyone noticing. If your song compliments the trills and tremolos of the regent's song, its hard to tell you're singing at all. This is a chance to exercise those unused vocal chords and learn how to sing on your own.
The dance of ascension is breathtaking to behold. It starts as any dance does, with the only sign that anything special is about to occur being a strange sense of calm in the demeanor of the right-hand-minion who has been called to dance. The regent typically has no idea this dance has started until it is underway. The minion moves in provocative ways, communicating with the dance a vision for the hive which is initially in line with that of the regent, but soon diverges into its own story. At this point, the regent would love to stop, but it's too late. Her song has already brought a sense of awareness and energy to the entire hive as a side effect of dancing with the suitor. To stop now would undo all of her hard work to keep the hive together. She has to keep singing until she can subdue the suitor. Many times, this happens. The suitor tumbles off of the null, and in a heart beat the entire hive descends on his body and shreds it. However, on occasion, this simply doesn't occur. The suitor understands the regent's mind too well, and she simply cannot trap him.
Then, something magical happens. The suitor stops moving. Or at least, perceptibly stops. Now the battle of wits begins. His most imperceptible movements are amplified by the shape of the sound front such that the regent must adjust her song to match his movements or lose control of her hive. However, the suitor seems to be one step ahead. Every time she tries to move the null off of him, his position is perfect to shatter the hive unity if she doesn't converge it back to him. They may stand ostensibly motionless for several minutes, her song crashing all around him, but never able to shake the null he has put himself in.
Then, when she isn't listening, he begins his tune. It's much quieter than hers. While he's been practicing, there's no way to practice true combat volumes without someone noticing. However, this is not a song of brawn. Its a song of finesse. It slowly distorts the sound front around the other hive members who, energized, respond ever so slightly. Then, in a singular moment, the regent bows her head to one side, trying desperately to keep her minions in control under her field by shifting the position of her singing organs. But a head bow is one move within the minion's dance, and it leads to another, and another. The suitor stands still, as the regent once did, while the regent is forced to dance as a minion until she ceases her song entirely. In a show of simultaneity which would leave any drum line or army drill corps to shame, every minion rotates ever so slightly to attune to the suitor's song alone. He is now the regent, having demonstrated that his grasp of the need of the hive far outstripped the dethroned regent. She is now his right-hand-minion.