Framing wall on uneven joists?
	
	
		We are building a wall (our very first) as part of our DIY kitchen renovation. There is no subfloor in this spot, and the joists that we are nailing into are not level -- the 3 joists in the middle of the wall are about 1/8" higher than the joists on either side. We tried to level the joists with blocking but couldn't get them to a uniform height. We were thinking that it would be easier if we could just cut the bottom plate into 3 separate sections, which would be at different heights, and then cut the individual stud lengths accordingly. Does this sound okay? Or will it hurt the structural integrity of the wall? It is non-load bearing, but it will support our main kitchen cabinets and cement board, so we do want it to be sturdy. Any other thoughts? Can shims be used in this application, or are they not strong enough?
We have the same problem with the top plate (there is a header in the way that is lower than joists on either side of it) -- but here we thought that shims might be more appropriate since they will not be bearing weight.
Thanks in advance for any advice you can offer!