[kevmo314]

> Ideally we want to preserve as much of the initial distribution (i.e. do as little chopping and changing) as possible.

I was thinking through the post that this sounds like a straightforward problem and it is: https://stackoverflow.com/a/5953133/86433

Except the introduction of an "ideally" optimization condition turns it from a straightforward transform into something requiring a linear programming solver. I wonder if the resultant algorithm is actually any simpler though...