I hate to tell you that both of those styles are created with heat. That's why they look so perfect. However, I agree that you will have no problem achieving a flatter top without the clips and plopping. Most people complain about the opposite.
I don't do this because I want less curl, but more just as a nervous habit. A lot of times throughout the day I finger comb through my curls and it definitely loosens them up. I can style as usual and get away with a decent amount of finger combing before it gets too frizzy. Maybe you can try that!
2b/c wavy modified CG since July 2012
medium texture, normal porosity, normal elasticity
hair likes protein, doesn't like oils, easily OC'd
low poo: JCHCC, CJGCS
RO/co-wash/LI: YTCarrots, DB Pumpkin Seed
stylers: a bunch of stylers that are all pretty much the same (KCCC, UFDCM, CRCM, CKCJ) or ArcAngel if I need more hold
DT/PT: CJRM, CNPF