Eloise is right; you have those white bits (commonly referred to as "halos"

because you are allowing Photoshop to make the alpha for you, based on the image transparency. This causes any semi-transparent pixels to be blended with white, and gives you the halo.
You need the 7.0.1 patch, so you can make the Alpha using a channel. You can find it
here for the Mac, or
here for the PC. The one you want is about half-way down the page, in the Version 7.0.1 section, and is called "Adobe Photoshop 7.0.1 Update," released on 8/22/2002.
To make an alpha channel, just hold down command/ctrl and click on the thumbnail in the layer palette. That will load the non-transparent pixels as a selection. Then Save Selection, and you'll have your Alpha. (You don't even need to go look at it, if you don't want to.) If you have more than one layer, hold down the shift key as well, and click on all of them before you Save Selection.
Place a layer with a dark color at the bottom of your layer stack, and the semi-transparent (anti-aliased) pixels will be blended with that, eliminating the halo.
Eloise, you can easily change the display so your transparency is black, and opacity white. On the channel palette, at the top, there's a flippy triangle. Make sure that you have an alpha (it can be blank, but it has to be there,) and choose Channel Options from that menu. (If you don't have an Alpha channel, that option will be grayed out.)
Click the radio button for "Color Indicates: Masked Areas" (instead of "Selected Areas,"

to return the setting to its default. That's a global change, by the way. All your new images will now show transparency as black, and opacity as white, although your old ones will have to be manually reset if you want them displayed the same way. (Which I recommend, by the way.)
Hope this helps!