Beyond the hanging paper test is my personal favorite.....The Hanging Toilet Paper Test.
The idea is to take a length (4 - 5 sheets or so of the softest/fluffiest TP (I prefer Charmin) and while hanging this sheet from your non-dominant hand make a quick downward cut into and through the lowest 2 sheets all the way out of the bottom.
If you manage to cut through the TP without tearing it while making a clean smooth pass and without tearing any part of any sheet along a perforation then you got one really sharp knife.
It is acheivable but it does take some work. I can do this with my Marble's 7" (10"OAL) Trailmaker partly because I can get this sucker really sharp by leather honing the convex ground blade. No swoosh here but rather a
wiff sound. Swwweeettt!!!

Now what was amazing to me was that my straight out of the box my SERE 2000 performed this test perfectly with it's factory sharpened edge. In my experience this is very rare to see . I did later dull the SERE's blade by trying to cut through a plastic-ish tip of a Blistex tube. I couldn't believe this happened because I've cut so many really tough items with this knife and then it goes and meets it's match on a tiny tube of Blistex. I mean what's this tube made of anyway? That Blistex tube was like Kryptonite to my Super SERE.

Go figure? After I resharpened the SERE I did the free hanging TP test again and it failed miserably yet still shaved hairs. Hmmmmmm....
This then left me to go to the leather hone. After honing it performed only marginally better. It will almost do the free hanging TP as good as new but yet it's still not the same as it was right out of the factory box.
Another knife that I experiment on regularly is a Puma Protec with 440C blade. Out of the box it never cut good. I free handed on Arkansas stones but that did nothing. Then I used my Sharpmaker and by using both sets of rods 3 times (using all corners and flats) I was able to rip through the TP. Ahhh.....results.

Then I went to the leather hone and whallah!!!
"Wiff" sound again.
So, I'm not sure what I can deduct from all this other than some dull, out of box, blades (good and not so good steel) can sharpen up sup real nice while some sharp ,out of box, blades (good and not so good steels) can never be brought back as good as the original factory edge. Of coarse my sharpening skills could have a lot to do with it too.
Plus, some blades seem to work with better in the free hanging TP test with a coarser grind rather than a polished grind and vice-versa. I know there's a lot more to all this when you start talking scientifically but I know the patterns that I see myself.
Either way, try this test on a few of your knives and see if they're as sharp as you actually think they are. Compare this test with the results from other tests. I think you'll be surprised.
Just my 2 cents.....
--The Raptor--