I'm not really sure what you mean.. do you mean noise in the shadows/ dark regions of the first logo (darker lines around the "1" part) or do you mean the noise in the reflections?
If it's the dark orange parts, this happens when I try to use and modify logos with backgrounds, so due to the cutting out/ resizing this happens. I'm hoping in a way that people use smaller logos in their fastdials then are shown on this site, so those imperfections are not seen.
If you mean the "noise" in reflecitons, thats how it is because it's transparent, so the background is "seen" trough.
Anyways, I gave it another try with the first logo, hope you like it..

The one with the bold border is the old one, new one is the second logo.
I'm pretty sure that by shadow you mean the flipped transparent reflection of the logo, right? Again, thats not white dust "added" into it, it's the backgroud thats seen through it. If you look at the logo on the black background, black "dust" will be seen. Look at the example with black background:


Think of it as the logo is object placed on the glossy surface, so it reflects toward the viewer. It's reflection is gradually transparent, from almost opaque where it's the closest to the object, to the full transparent where it's closest to the viewer.


If you want a shadow it would look somthing like this:

But i'm not a big fan of making logos with shadows as they look massively different on different backgrounds...