I think you actually provided a good start for the correct answer right in your question (you just need the correct syntax). I had this exact same problem, and putting DISTINCT in a sub-query was indeed less costly than what other answers here have proposed.

select a.FirstName, a.LastName, v.District
from AddTbl a 
inner join (select distinct LastName, District 
    from ValTbl) v
   on a.LastName = v.LastName
order by Firstname

UPDATE (2023): Denis M. Kitchen's answer can be better than my answer from a performance point of view, but it's important to mention that his query can produce a different result than mine, if the same (FirstName, LastName) combination appears in more than 1 record in AddTbl (see the example here ). This can be either good or bad, depending on the particular use case.

MY ORIGINAL ANSWER (2011):

Try this:

select distinct a.FirstName, a.LastName, v.District
from AddTbl a 
  inner join ValTbl v
  on a.LastName = v.LastName
order by a.FirstName;

Or this (it does the same, but the syntax is different):

select distinct a.FirstName, a.LastName, v.District
from AddTbl a, ValTbl v
where a.LastName = v.LastName
order by a.FirstName;

You can use CTE to get the distinct values of the second table, and then join that with the first table. You also need to get the distinct values based on LastName column. You do this with a Row_Number() partitioned by the LastName, and sorted by the FirstName.

Here's the code

;WITH SecondTableWithDistinctLastName AS
(
        SELECT  *
        FROM    (
                    SELECT  *,
                            ROW_NUMBER() OVER (PARTITION BY LastName ORDER BY FirstName) AS [Rank]
                    FROM    AddTbl
                )   
        AS      tableWithRank
        WHERE   tableWithRank.[Rank] = 1
) 
SELECT          a.FirstName, a.LastName, S.District
FROM            SecondTableWithDistinctLastName AS S
INNER JOIN      AddTbl AS a
    ON          a.LastName = S.LastName
ORDER   BY      a.FirstName

add "distinct" after "select".

select distinct a.FirstName, a.LastName, v.District , v.LastName
from AddTbl a 
inner join ValTbl v  where a.LastName = v.LastName  order by Firstname

It's not the same doing a select distinct at the beginning because you are wasting all the calculated rows from the result.

select a.FirstName, a.LastName, v.District
from AddTbl a order by Firstname
natural join (select distinct LastName from
            ValTbl v  where a.LastName = v.LastName)

try that.