How do I strip 30 guage wire?

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I have made Litz speaker wire by twisting together 10 strands of 30 guage kynar coated silverplated solid copper core wire from DigiKey. If I melt off the ends it leaves a blackened residue on the wire (not to mention the noxious fumes). How do I strip the coating off cleanly so I can solder the strands together?
 
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