There are very few "real independents". Most of them consistently fall into one party or another in their preferences eventually.
What I prefer is "independent" thinking.
...and fall back out, methinks.
I liked Bill Clinton's rhetoric on the campaign trail when I was young and naive; I then leaned strong R until the Rs chose morality over fiscal restraint. Now I'm split between the Rs' unwillingness to treat foreigners as equals and the Ds' unwillingness to trade with foreigners fairly. I think my ideal would be to have a D prez with an R legislature. Fat chance of that.
A lot more people call themselves independent than are actually independent, tho -- that's for sure.