Is missing match in autocomplete feature counter-intuitive?

Our application provides a way for administrators to authenticate as a specific user.

It provides a text field to type a username you want to authenticate.

When you type 4 letters or more

  • the autocomplete list appears with a list of matching users you can authenticate.
  • the Login button becomes enabled

Unfortunately, there also users with shorter usernames (of 3 or less characters). So when you type "patrizio", you will see autocomplete list with "patrizio", but when you know a user al and you type "al" you will not see him on the list.

Doesn't that give people a false impression that there is no user "al" in the database?

-EDIT-

A solution would be perhaps to:

  • for 1 letter typed show only matching 1 letter-long usernames,
  • for 2 letters typed show only matching 2 letter-long usernames,
  • for 3 letters typed show only matching 3 letter-long usernames,
  • for 4 letters or more typed show matching 4 letters-long or longers usernames