Once upon a time, there was a commercial goop called "Strip-X" for doing this. Just dip the end of the wire in it, wait a few seconds, and wipe the softened enamel off. Worked great! I think GC electronics sold it, but haven't seen it in years, so it probably contained some really nasty substance that got banned at some point.
Some folks claim good results by placing the wire end on an aspirin (not acetaminophen or other) tablet, and heating with a soldering iron, melting the wire down into the tablet. This only seems to work on some insulation formulations, not all of them. And it stinks...
If you aren't dealing with heat strippable "thermaleze" insulation, then scraping with a razor blade/scalpel or sanding with fine grit emery paper is the way to go.