How do I save logo with glowing edges?

I'm trying to create a logo to be used for print that includes a graphic element with "glowing edges" in white. When I created it in Illustrator I couldn't get rid of the background when importing to InDesign. When I create it in Photoshop with no background, it imports ok on black, but the fade turns grey when on other colors. I need it to be consistent wherever it's placed. And I rather do it in Illustrator so enlargement is not an issue. Help anyone?

you will either have to do it in photoshop, with a pure glow and saved with a decent feathered glow on a transparent background, or do the glow in Photoshop with transparency and place it in a layer behind the vector art in Illustrator

i normally dont import when taking stuff from illustrator to indesign.. just drag the art work over and it should go without a background..