Usually make a PA on the downwind for another landing. It’s not that busy once you’ve got the gear up and reached your climbout speed for the flap setting you are going to use for the second pattern.
Why is that disconcerting to you? Is it just not knowing, or is there some reason that would concern you more than others?
Usually, it is spacing on the aircraft ahead that has either been reduced too far, or that they failed to clear the runway where the controller thought he would.
That exact scenario happened on my last flight into ORD in the weather, actually. American missed the hi speed exit. Thankfully, it was ORD (Chicago) and the controllers are AWESOME!
We got to about 100’ feet before American finally cleared, but ATC let us keep coming down, because American exited over a mile down the runway and managed to clear just in time. We landed normally, no one got excited, and the passengers didn’t know a thing! However, I RE-briefed the go around procedure as I watched it unfold, just in case.
:-)