LIKE Matching Question

I have a piece of code that uses LIKE matching to check for the existence of a set of characters in a string as follows

SELECT a.Name, a.Market
FROM Table a
Where a.Name LIKE 'DAVIEL%'

I have the following sample data in a look-up table

AddID Name_Full
100 DAVIEL
101 DAVIEL
102 DAVIELT
103 DAVIELT
104 DAVIELT
105 DAVIEL

When I write the above query, I want to exclude the AddIDs that have a Name_Full of DAVIELT. In the Name_Full column the only difference between the two strings is the "T" in DAVIELT.

Please note that it has to use a LIKE statement. The code is already written that way and I do not have control over it.

Any help will be much appreciated.