I put together that estimates the "correct" location for a data point in a really wide bin.  The way it works is like so:

1. For a supplied distribution, fit it with one or more functions [in this case I used 3 different exponential functions over pTjet = (0.2, 3), (3, 23), and (23, 47) GeV/c].
2. Calculate the mean within each bin using the relevant function.
3. And the new point is defined to be the mean.

And then, if the user wants, this process can be iterated using the new points.  Below shows the shifted data for our recently unfolded pi0-spectrum (only statistical errors are shown).