Since you want to get a new 4 string, and you want a thinner neck, in addition to the Peavey Fury suggestions, may I also suggest the Squier Sonic Precision bass. Don't let the inexpensive price tag fool you - the one I have is very nice. It's got the jazz bass spec'd neck and the one I have is very stable with nice fret work. Now, I will admit that I did mod mine. The one quibble I had is that because of the light body, there was a bit of neck dive. So I solved that issue by changing the bridge to a Hipshot "A Style Fender Mount" bridge, and also replaced the tuners with GOTOH Res-O-Lite gb350s. Perfect now. And even though I found the pickups to be satisfactory, I did swap them with a Seymour Duncon SPB-1. I'm all set.