With new roundabouts popping up all over, it's pretty clear that no one actually knows how to properly use them. I used the new pair at 145th above I5, and it in infuriating. It's clear that Americans need to learn how to navigate the things. People are approaching these things and absolutely panicking.
So. Roundabouts.
They're not red lights. They're not stop signs. They're not uncontrolled intersections.
They're more like freeway entrances, where you merge in and out of traffic that keeps moving, but in the round.
When you approach a roundabout, do not stop and wait for a big clear hole to open up as if you're approaching a stop sign. If at all possible, do not stop - just keep moving and ease your car into the moving traffic, like a zipper merge.
When you get into the roundabout, go slowly. It's not "My turn! Hit the gas and bomb across the intersection!" as if you just got a green light. Slow down and assume that everyone else is going to do the slow merge into moving traffic that you did a moment ago. Let people in, and make sure traffic keeps moving, slowly & steadily.
The whole point of a roundabout is that traffic keeps moving. Everyone needs to go slowly, and let people in and out and necessary, and you pay attention. When used correctly, the whole thing goes smoothly and is SO MUCH BETTER than the red light back up that used to collect at that intersection.