Using column alias in WHERE clause?

Is it possible to reference a column alias in the WHERE clause? 

I'd like to create a query something like this: 

SELECT cust_id,
CASE WHEN TRIM(UPPER(cust_name)) LIKE TRIM(UPPER( 'Joe Jones' )) THEN '2'       --SAME NAME    WHEN TRIM(UPPER(alias))
LIKETRIM(UPPER( '%Joe Jones%' ))   THEN '1'       --EXISTING ALIAS    ELSE '0'      --NEW NAME
 
END AS name_test
FROM customer
WHERE cust_id = 1234
OR name_test > 0
ORDER BY name_test DESC

When I try it, I get: ERROR:  Attribute "name_test" not found

If I remove name_test from the WHERE clause, the query still runs fine with name_test in the ORDER BY. 

Is there a way to reference the alias in the Where clause as well? This is PostgreSQL 7.3.

Thanks,
August