I think OP uses "normalize" to mean force the welfare distribution to approach a normal distribution. If so, I think there are interesting moral questions to answer as to whether this is preferable. It is certainly not pareto efficient.
Anyway, on to two (and as a response to zomg), I highly doubt that 100% income tax or "serious" government intervention is the optimal solution. Wealth stock is dynamic and either of these would force the wealth stock to plummet. Moreover, substantial transaction costs will eat away at the available stock of wealth.
Better instead to structure institutions to incentivize entrepreneurship and wealth creation and human capital investments, along with a minimal level of public assistance. There is a lot of focus among leftists on the "market failure" roots of poverty; these individuals ignore that "government failure" is often just as strong a force. If the rightsizing of government and the creation and refinement of appropriate institutions is pursued, "poverty" - by which I mean the condition of being unable to meet certain basic needs like food, clothing, shelter, etc... - will decrease naturally.
The trend of history suggests that the poor are getting richer in two ways. First, the relative expenditures on basic needs has been plummeting: http://3.bp.blogspot.com/_otfwl2zc6Qc/TC9NcrJvG0I/AAAAAAAAN3Y/S8hwBzi_3uk/s1600/food.jpg. Second, quality increases in goods and services almost consistently amount to "real" wealth improvements for each successive generation of impoverished.