A) Anticipate up front what other person needs to hear and say it all
B) Rapid adjustment to ideal info requirements as your model of their knowledge/interest is live-updated.
But the trick people seem to miss is that interrupt-denies and counter-interrupts make the whole thing possible.
When I'm talking with someone for whom this style is natural, there can be many very rapid small gestures to interrupt, which sometimes are accepted and sometimes are rejected by a small "just let me keep going, you'll see why" gesture. Each of those gestures takes a fraction of a second (and generally does not actually break flow of speech, just eye contact + a little head motion), and conversations employing them are far more enjoyable because information flow is near optimal.
On the other hand, when speaking with anti-interrupt people, I often get so bored it's hard to pay attention because either 1) they left something out that I wanted to ask about so I can't follow what they are saying, or 2) I already had a thorough understanding of something they insist on giving a long explanation of.