I have a friend who was on a budget a couple of years ago when she started running, so she when online to search for best selection plus size sports bras and bought a moderately priced sports bra two sizes too small. Not the flimsy lycra spandexy stuff, but the really firm (almost non-stretchy) type that’s like a mix of thick cotton with just bit of lycra mixed in.
Even though she have lots of bras, She still love that one. She huffs and puff a bit to squeeze herself in (She puffs much less now, though) but she wears it on top of a regular non-padded bra and it’s like she strapped plaster around her chest (sort of like the movie Shakespeare in love).
She jogs on the road, facing traffic, she hates having all the heaving going on plus the discomfort of jiggling about. She said that nothing moves at all, so herlower body can speed up without worrying about her upper body speeding up (and down!) as well.