1. Go to http://musicbrainz.org/artist/71f6f5cc-cb53-4662-9754-1a934bb4928c
2. Pick any of the release groups which are credited as "Fats Waller".
3. Copy the name. (For example: After You've Gone )
4. Hit "Add release"
5. Paste the title into the title field
6. Hit next.
7. You should be at the release duplicates tab. Choose the offered duplicate release.
8. Hit next.

Note that the Artist on the single track has a magnifying glass, signifying that it is not being treated as an artist credit.

9. Hit "credits", to correct the artist credit.
10. Type "J. Lawrence Cook" into the "artist in musicbrainz" field.
11. Hit "credits" to accept the correction.
12. Hit "credits" to double-check that the correction worked.

Note that the "artist in musicbrainz" is once again set to the wrong artist (the artist credit).