...or you could use the graphic fade function to even out the levels before you normalize it.
When you normalize to 0db(peak), you won't get much in the way of results if the early part of your recording is peaked out. Normalize takes the entire wave into account.
Bean's suggestion is not bad either, but keep in mind that using RMS normalize can distort your music if not used with great care. Again, it takes an RMS average over the whole wave, so you're likely to have the same problem even if you use RMS.