T i m wrote
Rod Speed wrote

They arrived promptly (from Glasses Direct or some such), and
I tried them all on for a test but have never actually worn any
of them since because even though they are frameless and
not particularly thick, they are heavier than my ReadySpecs
(so can fall off if working and I face downwards),

That's because you havent got the arm length right.

Is that something you specify when you order

Yes with the best of the online sellers. Its marked
on your current glasses arms with most glasses
so it should be easy to specify the arm length
you want from the ones that don't fall off.

(in which case I would have when did)

Not all allow you to specify that.

or can adjust once you have them?

You can with many of them with a hot air gun.
That's how they adjust them at the optometrist.

How do glasses with completely straight arms stay on peoples faces?

Those have more force towards the head so they grip better.

I generally have to bend or otherwise adjust the arms
outwards to reduce the pinching pressure on my head,

That's because you are big headed {-(

With the best of the online sellers you
can specify the width of the frames too.

even when that only results in the arms ending
up mostly parallel when fully opened.