How to delete a signature from a key with delsig?

[Max Burley]

I have two keys: 
- a personal key (used to sign this message); and
- a business key.

Inadvertently, I signed the business key with the personal key. Trying
to remove that personal signature with delsig fails.
Bringing up the business key with "gpg --edit-key <key_name>" gives me
the "command>" prompt, at which point entering "<UID (n)> delsig" runs
without an error message, but the personal key signature is still
attached to the business key when I run "gpg --list-sigs <key_name>".

Am I missing something terribly obvious here?
Max Burley
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