I use Elements too! The best way I've found is when you are drawing the line art (make sue you have a sketch layer first), zoom in are far as you can. This Tutorial is really helpful too (It says it a coloring tut, but she shows you how she does her lines too).
I use to use Photoshop elements as well and had the same issue. Not too long ago I switched to CS 4 and no longer have that issue. I would recommend if you cant afford to buy a new program that you try using higher dpi as well as a larger canvas. Once you finish your line art, you can scale it down.
What program are you using? PaintTool SAI has a really good stabiliser that gives much smoother lines, but if you're looking for a free alternative, I suggest FireAlpaca, it's free and the stabiliser works as well as SAI's. Another option to consider is using no lineart. When I just started digital art my lineart was super sloppy (you can't imagine...) so I did lots of lineless drawings, it took the stress off having to make a meticulous lineart, and it still looks pretty good (: My lineart's gotten much better (it actually doesn't hurt to look at it anymore) but I still prefer lineless because it's so hard to make super clean lineart OTL