transparency?

In Photoshop I make images transparent by selecting them, pasting them into
a new file with a transparent background and doing a GIF89a export. As far
as I know, I do it the same way every time.  

My web page background is white. Some of my images are transparent against
this white background. But others have backgrounds that show slightly, in a
different shade of white, or a darker shade of any other color I put them
against. 

What am I doing wrong?

Thanks, Allie

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