Query with DISTINCT - logic?

[P. Boomer]

I've got a small query going that looks basically like this:

SELECT * from `mydb` WHERE `IDENTIFIER` = $variable

The $variable contains a value the user chooses from a coded dropdown.

The database I am working with contains multi-thousands of entries - BUT - there are many duplicate entries where ONLY one field (EMAIL) is different from the rest:

EMAIL ADDRESS COMPANY NAME STREET IDENTIFIER
[e-mail] 23 Elm Street Acme Investing San Diego 12345
[e-mail] 90 Oak Street Blarney Capital Berkeley 12345
[e-mail] 90 Oak Street Blarney Capital Berkeley 12345
[e-mail] 90 Oak Street Blarney Capital Berkeley 12345

I want to select all records, where `IDENTIFIER` = '12345', AND
which have a unique address. The problem is that the database has many listings at a single addresses, and I only want one record per address.

I think I could write this if I could figure out the logic!

TIA for your usual expertise!