The trick lies in:
1) keeping the leaves as intact as possible while you peel away. What was the problem with the leaves I peeled below (bottom right)? Yes it seems intact but not separated finely enough. Leaves that are not peeled sufficiently often result in a bitter, sappy brew.
2) Investing a little bit more effort into making sure that your leaves look as evenly peeled as those in the top photo. Shake it apart if you have to try to obtain finer bits, but be gentle in your ways. Ensure that no lumpy parts are left behind and your plate of precious tea leaves will seem more plentiful and harmonious.
Try this at home and notice how much sweeter your pu'er tea actually is.