If I were a redistributionist, here is what I might propose: A large fixed payment to every citizen, paid at the beginning of every month, financed by a proportional tax on consumption, such as a value-added tax.
One very eminent source emailed me and he wishes to stress that the (relatively) high level of the European Gini stems from higher levels of unemployment, whereas the relatively high level of the American Gini stems from the rich being very rich.
One story that might tie this together is that the U.S. has lower marginal tax rates, so we wind up with more people working, and some very talented people working very hard. If you're equally talented in Europe, you would take more of your income in the form of leisure, because the tax rate on market income is high.
The point of this story is not I think it's true (it could be.) The point is that in this story, the pre-tax distribution of income is a function of the tax system. So be careful about treating the pre-tax income distribution as some Exogenously Given Thing (EGT), and be careful about treating post-tax income as a separable function of this EGT and the tax system.
My general feeling about "our" income distribution is Lose the we. If you want to do something for poor people, then do something for poor people. Advocating a higher marginal tax rate on high-income people is not exactly an exercise in selfless moral courage. (If you are a high-income person yourself, you can always donate more of your own money to the government if you think that's the right thing to do.)