SELECT *
FROM People
WHERE Name like '%Franklin%' and Name like '%Linsey%'
[download]

Actually, I need AND. [...] Using OR would return a much larger result set than I was looking for. [...] So, AND helps narrow the search.

Just a thought: You might get the same result with OR by changing the search terms.

SELECT *
FROM People
WHERE Name LIKE '%Franklin%Linsey%' OR Name LIKE '%Linsey%Franklin%'
[download]

I have no idea what difference in performance this will get out of your database. I'm quite sure there will be a difference. Talk to your DB admin.

Another thing that I've learned from an Oracle guru is to avoid the LIKE operator where INSTR (other databases may call it POSITION or STRPOS) is sufficient. The reason behind that is that it is quite easy for an RDBMS to optimize (i.e. create an index) for a substring search, but LIKE most times requires a slow full table scan, operating on a search pattern. Again, talk to your DB admin.

SELECT *
FROM People
WHERE INSTR(Name,'Franklin')>0 AND INSTR(Name,'Linsey')>0
[download]

Alexander