i have a les pual custom(in white with gold hardwear) with a bigsby trem
if i use the trem the guitar goes horidly out of tune

i have looked at sperzels
and grovers
heard good about both, so just go with what looks the best with your guitar. also look at gear rations too, the higher the gear ratio, such as 12:1, 16:1, 18:1, and so on, the better you can tune it to the exact pitch.
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FWIW, I think Schallers are easier on your fingers.
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Go for Sperzals i put them on the guitar i made and im glad i did as they are really smooth and really well made.
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You must be really, really using that Bigsby hard to get a Les Paul out of tune that easily. They're designed for subtle vibrato rather than whammy.
I don't think there's an awful lot of difference between the performance of Sperzels and Grovers...might really come down to looks.
Sperzels, by far.
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