Browser URL desktop icons display 14x14 on 40x40 white background

The URL picture icons (the favicon designs) on my desktop display in size 14x14 pixels (tiny) on a 40x40 pixels white background. This is when I have medium size icons. Similar phenomena appears when scaling icon size up/down. I have searched extensively but not found the problem described elsewhere. System is Win 7 64 SP1 and newest browser versions as of today. It is quite annoying. Not really a good user experience on a small HD screen.

Further description:
- URL icons earlier displayed only as white "sheets of paper". I got to where I am now by refreshing each URL icon on the desktop by re-adding the icon to the desktop, dragging it from the FireFox URL line ('copy and replace'). I have tried same approach with IE 10 and Chrome while having each of these browsers as the default. They don't place any favicon designed URL icons on the desktop, only generic IE or Chrome icons - but in full size as they should be.
- I have tried deleting the icon cache. which makes no difference.
- Installed the program IconPackager and changed Windows default icons to something new and then back again. For someone this helped with a different icons issue. In this case it made no difference.
- Windows icons behave as they should. They are not getting smaller, nor are they displayed on white background.

Help on this issue will be appreciated.

Create a new user account and see if that desktop has the same problem.

Clear out your Icon Cache.

Icon Cache - Rebuild

Thanks for these suggestions.
@UsernameIssues: No difference with new user account.
@Gary: Already tried that (as mentioned above).

I should maybe mention that the machine is freshly installed. Setup was made using Windows Easy Transfer from my other Win 7 installation which has all the URL icons displayed as 'sheet of paper' icons (no favicon icons). On that machine, however, the 'sheet of paper' icon cannot be replaced by overwriting it with a fresh one dragged from Firefox to the desktop.

Look at the attached image and make your settings using the one circled in red

Hi Gary. I changed and restarted (I had "Let Windows choose"). No change. I also tried to reset the URL file association value in the registry (linkfrom description of IconCache.db-reset which you linked to above). This is a tough one, it appears ...

I do not place site or url Icons on my desktop,. I use bookmarks and the Bookmark toolbar for that. If they are just site Icons. Bookmark them and then remove them from your desktop.

Gary, thanks for your suggestion. You may be right, could be a bit neater. However, then URL shortcuts don't work across browsers. Also, I sync the computer with another one and a cloud drive. Further, the approach I use enable me to build history that lives on, independently of computer/platform. Have done it this way for a very long time and would like to get it working with icons of a reasonable size.