So....if you get a Tele with a humbucker in it, and one single coil pickup, instead of the lipstick/bridge pickup style, is that really throwing out the point of getting a Tele for that classic Tele "sound"?

I have a Les Paul that I love, and I'm looking into getting a Tele. But I wonder if I should lose the humbucker sound completely on the Tele, or if it's still possible to be a trad-sounding Tele with a double-coil in it, because I still love 'bucker tones.

In terms of the Tele 'twang" and "snarl" I guess--would the humbucker put that Tele tone off-limits as a result, and make buying the guitar for that reason be pointless in the first place?
I think you would lose it. I have a spalted maple tele with two humbuckers but the bridge pickup is a coil tap. Most people tell me that it doesnt sound like a tele and I agree but I can make it sound pretty close. That guitar is super versatile, it can play anything. ****ing amazing guitar.
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My Deluxe comes with dual humbuckers, but it seems to me like the bridge pickup does a good job of replicating that Telecaster tone. If you really want both, I'd say buy a Tele Custom, which (I believe) comes with a bucker at the neck position and a single coil in the bridge, which is my personal preference. Or, drop a bucker into a standard tele. Heck, if you wanted to keep the single coil sound accessible on both positions, you could route a split.

I'm not sure if Fender stock buckers can be split very well though. I'm still looking into whether its possible and how I'm going to go about getting that done.
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I have a Tele with 'buckers in the bridge and mid positions... It still sounds like a Tele, kinda. Sounds more like the bastard child of a Tele and a Les Paul, but who's complaining?

Without the regular SS pickups a Tele will sound different; however, if you know which Tele twang you're after (bridge or neck) then you can easily choose a guitar to fit that... Particularly if you're after the Tele's bridge tone. The classic versions with the neck bucker are still PURE tele in the bridge position. My bastard tele is still pure tele in the neck position (which is more what I was after).

The best option for your issue would probably be to get a standard issue tele and throw a mid-output hotrail in the bridge with a tap-coil. That should give you all the tones you're after...