A well-known result by Palamidessi tells us that $\pi_\text{mix}$ (the $\pi$-calculus with mixed choice) is more expressive than $\pi_\text{sep}$ (its subset with only separate choice). The proof of this result argues with their different expressive power concerning leader election in symmetric networks. Later on, Gorla offered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of “incestual” processes (mixed choices that include both enabled senders and receivers for a common channel) when running two copies in parallel. In both proofs, the role of breaking (initial) symmetries is more or less apparent. In this talk, we shed more light on this role by re-proving the above result|based on a proper formalization of what it means to break symmetries — without referring to another layer of the distinguishing problem domain of leader election. Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reasonable encoding from $\pi_\text{mix}$ into $\pi_\text{sep}$. We indicate how the respective proofs can be adapted and exhibit the consequences of varying notions of uniformity and reasonableness. In each case, the ability to break initial symmetries turns out to be essential.