Sometimes when I mount a tire on the rim, and then spin the wheel, there are noticeable hops in the tire as the wheel spins around. That is, at some points the tire is further from the rim than others.
I've had this happen with road tires and mountain tires, although of course it's more noticeable with mountain tires since the tires are much thicker. In all cases the rim is round, this is not a function of the rim having a vertical hop.
I don't know how much this is a problem - perhaps the bumps aren't going to be felt while riding because weight on the tire will compress it to the same spot no matter if it's further from the rim or not. But I suspect otherwise.
What causes a tire to have a vertical hop when mounted on a rim? Are some tires more likely to get this, because they have tighter (or looser) beads? I don't know.
I usually try to find the low spot, and, starting from the opposite side of the wheel, pull more tire toward the low spot. But this is very hit-and-miss.
Are there any better, more confidently surefire ways to avoid hops in tires?