PNG-24 images have slight white halo when saved in CS5 but not 7

Question

I've been using Photoshop 7 for several years to create artwork, and export that artwork as transparent PNG-24 images for use on the web, to be included in other images, etc.. The images usually need to be drasticallly reduced in size when I'm done with the coloring and shading (usually to around 20% of the original size, for a final size of around 500px high or wide), and the resulting smaller PNGs Photoshop 7 created always had clean and crisp edges.
I've been looking at finally making the move to CS5, however, and so I tried working with another image in the CS5 trial. At first everything seemed fine, but when I went through the Save for Web dialog, shrank and saved the image as PNG-24 and then opened it again to paste the result into another image, there was a slight whitish halo around the outline. I'm not sure why this happened as I don't remember using output settings any different from those in the 7 dialog; I tried changing the quality from bicubic to the other options, but nearest neighbor obviously made the outline look messy and the other options didn't have any noticeable effect (though I didn't really expect them to).
As an example, here are links to the image I recently created on a background: the first is what CS5 seems to do (add the halo); the second is technically a much larger version of the PNG with cleaner lineart (since I didn't shrink it first), but scaled down to the right size, since I don't have 7 itself to try re-saving the PSD.
Image with Halo (CS5 output)
Image without Halo (7 output)
Saving as PNG-8 or GIF leaves clean outlines if I turn off Matting, but I need the subtler color shifts of PNG-24; JPEG obviously isn't an option because I want the transparency.
The last time I noticed this with a trial on an older computer, I simply reinstalled Photoshop 7 and continued working with that. This newer computer is 64-bit, however, and I can't install Photoshop 7 without jumping through a few hoops. I can do it if I must, as I don't need any of CS5's newer features that desperately, but I would like to move up to CS5 in general and so want to know if there's a solution to this before I just give up and go back to 7.
So I'm curious: is there a reason for this difference in behavior? Was this an intentional change, or is something wrong with CS5? I understand that there may not be much that I can do, as CS5's behavior does make some sense given the way Photoshop has to recalculate the image when resizing it, but 7's behavior, even if it is somehow "incorrect", is more desirable because the result is cleaner outlines. Is there a setting I can adjust, is there some sort of problem I can fix, or should I just go back to Photoshop 7 for saving this kind of work when I get the chance to reinstall it?
Thanks in advance for any insight you can give me; let me know if you need any other information.

Answer 1

Absolutely! Here are a few of the files in question:
and these that work perfectly for my client:
Thank you!