Just finished retrofitting a Jazz Bass. **Pics**
This bass started out as a "98 Fender Fretless Jazz Bass. It was made in Mexico and was about two steps up from the bottom of the line. I bought very cheap from a liquidator because I wanted to try fretless. Playing fretless never really suited my style, so the guitar just sat around collecting dust. My main bass is an '03 P-Bass Deluxe, but I wanted a Jazz Bass to back it up, so I decided to rebuild the fretless.
The body is basswood, and fairly dense, so it was a decent start. The electronics are actually USA made Fender parts so they stayed too. I had two options on the neck; I could have had a luthier install fretwires or go with a new neck I chose the latter as the original neck was the weakest part of the guitar. I bought a MightyLite replacement neck as they are licensed by Fender to make them. I found a company that makes reproduction decals and bought their '65 Jazz bass decals to apply to the headstock. The neck was finished with natural oak stain for the "aged" color, and 10 coats of polyurethane and wet sanded between coats. Smooth as glass. 
I also installed a Hipshot bridge to replace the flimsy stamped steel original to give it more sustain. I finished it off with a Fender Custom Shop white pearl pickguard.
It turned out pretty well I think, and plays great. I'll try it out for real next weekend. Bellow is the "new" guitar and below that was what it originally looked like.
= new reply since forum marked as read
thought you meant one of these signing a little Ella or Torme
http://www.amazon.com/MOUTH-BILLY-BASS-SINGING-SENSATION/dp/B000F792BG
Billy Bass is on his own.
...You need not a proper fretless neck. A hot iron on the frets of even a cheapo bass will loosen the glue enough to pull the frets free with needlenose pliers. Restring and presto, fretless.
I know this because I tried it with an old junker, fully intending to putty in the gaps left behind by the missing frets. Turned out that part wasn't necessary.
You know, I can play fretless, I was just never happy with the sound. I think part of the problem is that I have short fingers and my muscle memory wasn't always on target so I'd have to constantly be hunting for notes and that may have contributed to not liking the sound.
Maybe I'll try again some time.
bluesbassman 
It looks awesome....
Of course I didn't understand some of the terminology ....
Then it made something click!
I remembered something crazy you wrote in times past...
I had to seach...
Isn't it strange how our minds work? A post from long ago came to my mind...
http://www.democraticunderground.com/discuss/duboard.php?az=show_mesg&forum=105&topic_id=8515203&mesg_id=8515229
You do beautiful work...
Enjoy the fruits of your labor of love...
peace~
I remember that thread. It was a perfect set-up.
I've been playing the "new" bass a lot this evening. It's gonna be a nice back up.
The Hipshot is a great move. Like Mikey, I defretted a Japanese Jazz about fifteen years ago but never quite got the handle on playing fretless consistently well and wound up selling the bass.
I have a 1990 Fender of Japan Jazz that I had a luthier redo about a year ago. I'd added Seymour Duncan Vintage PUs ages ago, and when the plastic nut cracked I went whole hog - brass nut, Hipshot bridge and an Audere JZ3 preamp. It's a killer player's bass and a great backup for my Alembic. 
I think Fender Japan was actually putiing out better instruments than Fender USA for a while there.
I thought about converting to a string-through bridge setup like my Deluxe, but settled for the standard. Nice adjustment capability on the Hipshot, I had it dialed in for height and intonation in about 10 minutes.
Alembic makes awesome basses. Congrats on owning one!
Is it that you can do those slides like an upright? Nice work on the bass!
