Ragged edges on a logo

I created this text logo (attached) in Adobe Illustrator using Bodoni Sans Light font I purchased from MyFonts.

After having purchased the font I noticed that the edges of some letters ('O', 'C') come out very ragged. And when the logo is saved as a raster image, even at high resolution, there is even some fuzz on the edges of those letters.

I tried changing between different anti-aliasing methods, but it doesn't make much difference.

My client and I really like the font's style. Is there a way to fix this issue?