Removing unwanted white background in .eps file

Hello, I'm trying to save a logo designed in illustrator cs3 (mac) as an eps file with a transparent background. I do Save As > .eps, and then select the Tiff 8-color, Transparency options.

Unfortunately, every time I try to open the .eps file in Photoshop, it gives me an unwanted white background behind part of the logo. Any ideas on how to get rid of that white background and make the whole logo transparent?

Thank you.