Whenever I tune my recently restrung acoustic guitar, the bridge pins always seem to come and pop out on the higher strings, when I a few steps away from tune. Do I new new bridge pins?

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No dude, just hold them in tight and make sure the ball end is right up by the bridge pin when you put them in, no excess string, because if it slips it will pull the string out. Pull the string as hard as you can when you push the bridge pin in over the string, then it should all be tight enough for successful tuning and playing. Hope this helps :-)