Phono Pre Upgrade from Parasound JC-3?


Hi there,
I've owned my JC-3 for about two years and have no complaints about it.  It sounds very good, but I'm curious about upgrading to a preamp that would be a significant improvement.  
I've thought about upgrading to a tube phono preamp as I like the warmer sound of tubes and my amplifier is a Lyngdorf TDAI-3400.  
Given a budget of around $6K, what would you recommend?  
Thanks,
Peter
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I've heard that's a real good one.  Unfortunately it doesn't have balanced outputs.  I should have mentioned this in my original post.  The JC-3 has balanced outputs and when I switched to balanced cables after using standard RCA I was blown away by the improvements.  

I'm looking at the BAT VK-P6SE as it checks off the boxes and has great reviews.  Also consider a Manley Steelhead.  
Manley Steelhead= RCA only!  I highly recommend if your amp has RCA inputs you should give this unit a try. It will deliver what your looking for balanced or not. 
You will have to spend a lot more than 6K to get something noticeably better than the JC-3. Until you can spend 14K be happy where you are.
The John Curl designed Constellation Orion is $80K.  
Regarding the BAT VK-P6SE, I’d be concerned about the gain settings it provides. The "low" setting of 50 db seems likely to be too high for many high output cartridges, and the "high" setting of 55 or 56 db (depending on what document is looked at) seems likely to be too low for many low output cartridges.

Also, FWIW, like Millercarbon I am a happy owner of a Herron phono stage (the VTPH-2 in my case), which I use with a 0.5 mv AT-ART9 cartridge.

Good luck. Regards,
-- Al