City Index? Neither the code you posted or my code would even come near a "city" index if the Primary Key was the CustomerID column. 
Certainly, it wouldn't do a table scan if an index were present on CustomerID... Index Scan, yes... table scan, no.
The only reason I made the disclaimer about INT was because I didn't test it using VARCHAR. 
--Jeff Moden
RBAR is pronounced "ree-bar" and is a "Modenism" for Row-By-Agonizing-Row.
First step towards the paradigm shift of writing Set Based code:
________Stop thinking about what you want to do to a ROW... think, instead, of what you want to do to a COLUMN.
Change is inevitable... Change for the better is not.
Helpful Links:
How to post code problems
How to Post Performance Problems
Create a Tally Function (fnTally)