Two Sheets: "Data" and "List"

"Data" has a list of Cities in Column A.
"List" has a list of Cities in Column A and corresponding zip codes in
column B.
I am trying to lookup all the appropriate zip codes and put them to column B
in the Data sheet.

So far, I am using =LOOKUP(A1,LIST!B:B,LIST!A:A). It works, but if I have
two cities that are similar (i.e. Bellwood/Bellmont), it does not give me the
exact match. How can I get an exact match? I am pulling my hair out over
this one!