Here's what's always worked for me:

Hold the end of the wire in a lighter or match flame until the varnish
just flashes off. You may need to move the flame around a little to
char the whole length that you want "stripped."

Take a postage stamp sized bit of fine sandpaper, 600 grit or finer,
and fold it over once so that the sanding surface faces itself. Draw
the wire thru the folded sandpaper, squeezed gently between thumb and
forefinger, several times, turning it slightly between times until the
wire is cleaned down to clean copper.

It's actually quite quick and easy.

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Jim Adney
Madison, WI 53711 USA
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