Re: I think I want a Fly
Solspirit, if you can find an actual Fly or NiteFly, go for it. The lower-level models though (P-36?, PM-10 & PM-20, etc.), were imports, personally I'd avoid those. I had read that Joe Walsh, and Adam Dutkiewicz of KillSwitch Engage, have used Parkers. Like others have mentioned though, the only hesitation would be that Parker is no longer in business.
As far as being "too thin", the body of the guitar was very thin, not the neck. Carbon fiber fretboard, stainless steel frets. And that "hockey-stick" headstock. Ken Parker was definitely thinking outside the box. When my sons were taking music lessons, the guy at the shop would let me mess around with one of the Fly's. (LOL they hung those WAY at the top where a casual customer could not get to them! I think retail was over $2,000.) The Fly models had a very unique trem system, you could bend up or down, and it used a specific-weight leaf spring that you could change out to a heavier one if you wanted heavier-gauge strings. The Fly was neck-through, the NiteFly was bolt-on.
I ended up spotting a like-new Swamp Ash NiteFly, used at Guitar Center, and bought it on the spot. Other than the issue of no markers on the fretboard, which I was getting used to, it was the fastest, easiest-playing guitar I've ever owned. I believe it came with DiMarzios, and also had the Piezo function.
Sadly...

My younger son was learning keyboard, BUT, he said he
really wanted to play bass. The things we do for our kids, right? I had a few other guitars, and I wanted to get him a really good bass right from the get-go. Seeing as how the Parker had the highest resale value, I took the trade-in beating at GC and got him a super-nice Yamaha bass. The GC employee himself snapped up the Parker immediately. And so, a few years later, there the bass still sat, gathering dust, unplayed due to lack of interest; eventually we sold that for a loss as well. And at this point I will never be able to afford another Parker again...

oed:
Anyway, good luck, and if you end up getting one. please let us know how you like it!
