Opinions on nut slot height needed

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When I pull the string quite hard afterwards, it's almost back in tune Could it be that the nut slots are too narrow for the thicker strings

guitar nut slot depth The word may have come from the German Nut , meaning groove or slot doi:45MTC ^ Guitar Nut Repair article on the Guitar

guitar nut slot A guitar neck took a stock nut I knocked the hand-made nut off the There are lots of sizes in the set, good for filing tiny nut slots for guitars