Filter categories used with Custom Structure Permalink

I’m using a “Custom Structure” permalink setting:

http://mysite.com/%category%/%postname%/

However, when the post belongs to uncategorized, or to more than one category, this produces unwanted URL structures.

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Basically, I want to find out if I can run a filter on this so that “Uncategorized” and any child categories of Uncategorized are removed from this URL pattern.

Appreciate any help you can provide.

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