Classtime 

What is the trick to mounting these so that they are as round as the rims?

Lascauxcaveman 

Buy ones that don't have lumps in them.

But also, I've noticed that tires can go on unevenly on non-hooked rims, but not so unevenly they look or feel "lumpy." Paselas are notorious for having uneven sidewall color, are you sure that's not what you're observing; watching the gumwall appear to be going up and down? I've noticed that illusion a couple of times.

When I've had tires actually mount unevenly (looks like one part of the bead is going to pop off the rim as you get to pressure) I'd just deflate them back down to 10-15 PSI and sorta manhandle them back and forth until I was happier with the way they were sitting, then monitor them very carefully as I reinflated them to max pressure. Which would be about 70 PSI in the case of the rims I was using I finally got rid of all my unhooked rims, just so I could keep my tires inflated as hard as I like them.

dunelt_1954

Something else to look out for, is having a bit of inner tube pinched between the tire and rim. This will make for a lumpy situation, until it blows off. Deflate, and squeeze the sidewalls in to check for tube trying to escape.

Classtime 

I'll play more tomorrow with them. Some sections tend to seat lower and that is after deflating, messaging and reinflating.

JohnDThompson 

Deflate completely, then use a paste brush to apply a soapy water solution all the way around the bead on both sides (removing the tire from the rim is neither necessary nor desirable for this). Reinflate, and the soapy water will help lubricate the bead as it slides into position.

ramzilla

I've found that using the right size tube is critical for good tire performance. Using a tube too large for tire is a recipe for pinch flats and other problems. I get the smallest tubes I can find for my street tires. Inflate them just a little. Spray them with plain water. Place them inside tire. Make sure they're seated properly. Pop tire back on rim & you're good to go.

rootboy 

Good advice, John. That's what I did on my hookless Rigida rims. Along with checking at mid-inflation, and man handling, tweaking as I inflated to full pressure.
Full, LOW, pressure.

Velognome 

I've found that when a lubricant in not available, try inflating the tire to 3/4 pressure then with your thumbs on the sidewall, pushing the tire across the rim while working your way around the rim. Do this on each side then inflate to riding pressure. It seems to help settle the tire evenly around the rim.

Classtime 

So, I used the soapy water trick and that helped. While inflating, I needed to hold part of the tire away from the rim and things were better but not what I have come to expect from years of installing folding tires on modern rims. Seems that to do a really nice job I need an assistant because I cannot pull more than one section of tire while also inflating with the pump.

dddd

There are different problems that can crop up with tire beads not seating evenly around the rim.

Hooked-bead rims always seat the beads just under the hooks, so a quite-even seating of the tire is apparent unless the tube or rim tape is interfering with the bead(s) settling up under the hooks.

A non-hooked rim seats the bead around the outside diameter of the inside floor of the rim, adjacent to the smooth sidewall.
I've seen rims where the bead fit so tightly around the rim at this point that a portion of the bead never reaches the sidewall and instead stays in the central channel.
This can be the result of rim tape thickness at the inside shoulder or ledge at the base of the sidewall.
It can also be the result of a tight-fitting tire on a rim with relatively large diameter at the inside ledge. Continental wire-bead tires come to mind here.

Inflating tires on Schwinn's own steel rims can be a crap-shoot, whether or not the tire beads will pop up into the inside corner during inflation. Once pulled tight by pressure, further inflation may blow apart the tire or blow the bead over the rim's edge before the bead lifts out of the channel up to the inside corner! Even with a bead lubricant some tire and rim combinations have this problem, which makes getting the tire seated after a field repair particularly difficult if not impossible.

Some of the non-hooked rims are sized to a too-small inside ledge diameter unless covered evenly with a thick rim tape. The problem then is simply a very low pressure threshold where the bead has enough slack to simply climb over the edge of the rim and release (blow out) the inner tube.
Getting a thick layer of tape to seat evenly into the rim's inside corners against the side walls can be quite difficult, as the inflated tube pushes the tape into the central channel which tends to pull the tape away from the sidewalls. The type of tape used makes a big difference, and custom-cut width of tape sometimes allows this to work.
Weinmann and some of their old competitors are notable for having created the published notion that non-hooked rims can't allow full inflation of period 100psi wire-bead tires. But in fact the better-made rims had no problems with 100psi using wire-beaded tires, since their inside ledge bead-seating diameter was closely controlled for consistent bead seating.

Velognome 

These work really well. Over inflate, grab, rock and pull; deflate to proper pressure.

Aubergine 

A bit off topic, but this sort of fit issue can also happen with hooked rims. I had one set of tires and rims that just would not seat evenly. They were all good products; for one reason or another I had to adjust the position of the tire all the way around the rim. Once I got it in place and pumped it up it was fine. But I was certainly surprised at the mismatch.