Inequality is a pretty hot topic right now, especially in discussion of Charles Murray's latest writings as regards marriage, family, and inequality. I have some thoughts on inequality within the US.
First and foremost, I have no particularly strong passion for equality. But neither do I have a strong passion for inequality. Most who posture about inequality don't really have a real passion either---except one for moral posturing so as to aggrandize their social status. But for the purposes of this post, I'll take many at their word and postulate that they do indeed wish to reduce inequality within the US (the geographic boundary wherein the desire to reduce inequality exists is very very important).
To begin with, if one sincerely wishes to reduce inequality, one would pretty much shut down all immigration, legal or otherwise. Adding more people at the bottom end of the distribution just aggravates what you claim to wish to reduce. So supporting something akin to the immigration law of the 1920s is what is called for here.
The next item is more subtle. What you really need to do is motivate a higher birthrate in your upper classes while reducing it in the lower classes. If a rich man has, say, 4-6 children and a poor man has one or two, the inequality of the next generation will be reduced substantially, almost by definition. What you want to do is restructure the way child tax credits and exemptions work so as to motivate more fertility at the top of the distribution and less at the bottom. I suggest raising marginal rates in general but reducing the marginal rates by X percent per child when both parents of said child are still married to each other. The key is you want it remain highly significant even for those who earn millions of dollars but not to be a material incentive below the median. Should the parents divorce, I recommend reducing the benefit by 50%, and dividing that reduced benefit between the two former spouses equally.