I use a spring between thin parallels to keep them from falling over, also keeps chips from getting behind them; Brown & Sharpe made some more unusual parallels, Very thin parallels, maybe about 1/32" thick, and also Wavy parallels, also thin and perhaps 5/16" across the waves, spring tempered so they collapse in the vise when the part is clamped.
I prefer to use parallels of the wider sort if possible, I only go to the thinner varieties when working with thin parts. I have two pairs that I made as an apprentice that are sized so that the height difference is fairly small so that a pair of hold downs sit on the taller ones and the part on the lower ones, they are sized such that the part is near the top of an ordinary mill vise.