problems exporting in 16x9 with Sony EXCAM footage

I just finished editing my first video in Adobe Premier Pro 5 (before this I used Avid). Love the software! The only problem I have is that when I export the video it always gives me black bars above and below the footate, or in some cases, on the sides.
I´ve tried varios formats, including export same as source, and the black bars always appear.
(I´m in a Pal Project, but this also happened in a NTSC project).
The footage is SONY EXCAM full hd (1920x1080).
The bars appear on the same computer I am editing on, so this isn´t a case of the TV set.
What am I doing wrong?
(BTW, exporting with the h.264 codec because this will end up on the web, but what is the best codec to bring footage into AE?)
thanks!

If you have your Pixel aspect ratio correct (which is what Vince suggested you check) you might also be running across the problem that, while 16:9 HD really is 16:9, where as 16:9 SD isn't actually 16:9...

Because the aspect ratios are slightly different, you can get black bars.

There was a thread on the cow a few days ago about this, and Vince posted this link, which explains the problem: http://www.mikeafford.com/blog/2009/03/pal-d1-dv-widescreen-square-pixel-se...