Don't do it! Rounds on a Fender bass really narrow its range of applicability! Also limits the sweet spot to just one or two settings vs. all settings sounding musical. True of both P and J!

My Geddy Lee is about the opposite of what is needed for jazz. Even the 60's jazz bass w/ flats works on far fewer tunes than a P-Bass with flats. But there's a lot of stuff where it works better than a P.
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60th P-Bass, Select J-Bass, Geddy Lee J-Bass, Yamaha BB1025X
Eugenio Upright, Viking Bari, Select Strat, Select Tele, Am Pro JM, LP 57 Gold Top
Yamaha WX5, Hammond XK1c, Moog Voyager, DSI Prophet12