how to tell the difference between empty field and null field

Assuming a table such as this:

create table users ( user text, password text, name text, domain text
);

...and data such as this:

insert into users values ('frank','zCeZ6f2f.NUKU','Frank Farley','domain.com');

insert into users values ('joe','QJixz/XLXvio2','Joe Blogg','');

insert into users values ('sam','kAdhVr3URa4Y.','Sam Stooge');

Note that joe has a blank domain field, while sam has none.

I want to know what users don't have a domain specified in their domain field.
But the query:

select * from users where domain = '';

only shows me joe, and the query:

select * from users where domain = null;

only shows me sam.

So, I use:

select * from users where domain = '' or domain = null;

Here's my question: if I have a zillion records in this table, and it's indexed
by user+domain, how can I run this query without losing the benefit of the
index?

--
Alex Howansky
alex@wankwood.com
http://www.wankwood.com/