Had both of these for 30+ years...
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'85 Les Paul Custom. Got it used in late '86 or early '87.
The story behind it was when I was taking lessons on acoustic at a local shop my dad told me he'd buy me an electric if I met goals set by him and my teacher. Difficulty: used only, he wouldn't pop for a new one. The tags on the new LP's they had were $1100-1200ish. This was the best LP they had hanging in the shop. I had to have a Les Paul shaped object because Jimmy Page. He got it for $675. What a creampuff. No wear except for worming on the back from the WWF championship belt the previous owner wore. It survived teenage me who insisted on doing my own work on it despite hardly knowing shit from shinola about guitar maintenance. It sounds like a Les Paul and weighs as much as a Lincoln Town Car even with weight relief. All original except for strap locks.
But DAMNIT! I WANT ANOTHER GUITAR! A few years later I put feelers out at the same shop that I was looking for another LP, maybe a beater. One of the other guitar teachers said he had just the guitar for me. I got him down to $375 and was presented with an '80 Les Paul Standard that had been rode hard and put away wet. This guy had acid sweat and probably never wiped it down and maybe even pissed on it. It was gigged HARD. It was fucking disgusting when I got it, complete with rusted strings.
She cleaned up well and quickly became my #1. All original except for strap locks, replacement pick guard and speed knobs. I got it with witch hats, which I hate, and they're not right for that era. My guess is he swapped the original speeds to an early '70's LPC. When I play out, it's my stage guitar. Even though it has the same electronics and pickups as the LPC, this thing is just an unholy, filthy beast. Which suits me well.