SQL: ORDER BY two columns intermixed, not priority based

Question

I'm using mySQL. I have to order names of Contacts by Lastname but in the case that there is no last name, I order by firstname.

This looks like:

ORDER BY lastname = "", lastname, firstname

However, this makes the ones with lastnames appear at the top. The behaviour I'd like is to intermix the first and lastnames like they were from the same field.

Example (pretend these are names):

A,T 
Z,G 
A 
B 
C

Versus:

A
A,T
B
C
Z,G

Thanks

Answer 1

Use COALESCE and NULLIF:

ORDER BY COALESCE(NULLIF(LastName, ''), FirstName), FirstName

Answer 2

Try using Coalesce
Note: this would require you not to store empty last names using an empty string (ie "")

ORDER BY Coalesce(LastName, FirstName)

As Suggested in the Comments By adding FirstName to the order By list again you will properly order two people with the same lastName. Here is an example.

ORDER BY Coalesce(LastName, FirstName), FirstName