Same leading key column in unique constraint and nonclustered index - duplicate

These are two indexes on the table with the same leading key column. First is a unique constraint with additional keys: ALTER TABLE dbo.MyTable ADD CONSTRAINT UQ_MyTable_FirstColumn_SecondColumn_ThirdColumn UNIQUE NONCLUSTERED ( FirstColumn ASC, SecondColumn ASC, ThirdColumn ASC ) And the second is a single-key nonclustered rowstore index: CREATE NONCLUSTERED INDEX IX_MyTable_FirstColumn ON dbo.MyTable ( FirstColumn ASC ) Despite the benefit that the NC is smaller, I would consider it a **duplicate**. Am I missing something? No "de-dupe" script checker I am using agrees with me, so I am confused.