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I checked around and only found an 1/8" dremel router bit. I am making
a fretboard from walnut. Will the 1/16" dremel carving bit work to
make slots?

You'll be much better off using the correct tool for the job ... a fret saw:

http://www.stewmac.com/item/5745

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Last update: 9/30/07
KarlC@ (the obvious)