Pardon me for intrusion, but this is how I do it:
Sand the edges to the max grit you can find (I do it to 600 wet sand paper) and clean and dry the pieces. I use pencil butane torch for this, it needs a directional thin flame to succeed, use the torch along the edges in long moves (like painting), not keeping the flame on one place. Several passes with torch and all the little scratches are melted and cooled into a nice, see-through, flat surface.
It surely need practice (which I still don't have
), but pls, Mr. Fixittt, pardon me for intrusion, and pls. give us some more tips!
Cheers!