El cheapo basses fretting out at 1st fret

[pjmuck]

I picked up a couple of cheap basses off ebay to experiment with (one's a Flying V style and the other's a Les Paul style), and while they are both brand new and from different manufacturers I'm finding they're both difficult to set up properly. Both have the same problem: no matter how much I adjust the bridge, raise string height, or truss rod, both are virtually unplayable at the first fret position, as they're completely fretting out. I have not changed strings on them yet, but does this sound typical of a certain problem (Other than saying, "Yeah, cheap crappy basses"), i.e. poor nut cut, uneven fret height, crappy strings, etc.

[Pilgrim]

Try using a straight edge on them to see if they both happen to have a high first fret. That's what it sounds like - or a nut cut too deeply.