As a preteen, my favorite song in all the world was 'The Little Blue Man'.  I sang it to my kids and nieces and nephews through all the years and they would sit in the back seat on long trips begging me to sing it over and over and over!
 
One day when east met west, I found him!  My little blue man!  Yep!  There he sat, just waiting for me!  Since I started using this cleaning technique, I haven't used any of those old tubes but I couldn't part with them - hoping one day I would discover a way to REclean them so the edges would be smoother.  I did it!  I did it!  So simple, I don't know why I didn't think of it before.
 
This is a pic of the little blue man who is so symbolic of the years I was raising my children, old and new.

Old to the left:  top, the only way I could smooth him out was to add a dark dropshadow twice - first with '-1's and then with '1's.  bottom, the actual tube with the jagged edges.
 
New to the right:  top, used with just a soft shadow to one side for lighting purposes.  bottom, the REcleaned 'Blue'.  For some reason the entire little guy seems smaller, but just the edges are gone!
 
Now, I know we all have those old favorites that we picked up here or there that weren't cleaned very well and we all have those little attempts at cleaning from before we got GOOD at it.  Here's how to REclean some of them.
 
Open the tube and duplicate the image then just close the original or minimize it.
Zoom the view in a couple times until you can see the edge up close.
Add a new RASTER layer and drag the layer to the bottom in the 'layer palette' tool.
Use the color picker to pick up the color from the edge of the item.
Flood fill the lower layer to look like the image below, 'Merge Visible, then use the cleaning tutorial technique to REclean your tube.