SQL query to get the user, counting the minimum number of records I have an table with some records and a column LAST_EDIT_USER.
If I want to select all users with the number of appearances for every user, I would do 

SELECT   LAST_EDIT_USER,COUNT(LAST_EDIT_USER)
FROM     EDITED_ELEMENTS_TABLE
GROUP BY LAST_EDIT_USER
ORDER BY COUNT(LAST_EDIT_USER) ASC;


and this will return something like

NULL   0
user1  5
admin  7
USER2  11


How can I get from a SQL filter the user1 (with the minimum of occurrences) - excepting NULL?
LATER EDIT: or a list of the users with minimum number of occurrences
Add a WHERE clause to filter the rows where last_edit_user is null. Then put another query around it, to get the minimum count. Use this as a subquery in the HAVING clause to get only the ones with the count equal to the minimum.

SELECT last_edit_user,
       count(last_edit_user)
       FROM edited_elements_table
       WHERE last_edit_user IS NOT NULL
       GROUP BY last_edit_user
       HAVING count(last_edit_user) = (SELECT min(c)
                                              FROM (SELECT count(last_edit_user) c
                                                           FROM edited_elements_table
                                                           WHERE last_edit_user IS NOT NULL
                                                           GROUP BY last_edit_user) x);