Can't fully destroy session. Help!

I'm finishing an e-commerce site, but I've run into a problem destroying a
session at the end of a transaction.

The code I'm using, taken from a text book, is:

session_start();
session_unset();
session_destroy();
if( isset($HTTP_COOKIE_VARS[session_name()]) )
unset( $HTTP_COOKIE_VARS[session_name()] );

Now, I've tried updating this to:

session_start();
session_unset();
session_destroy();
if( isset($_COOKIE[session_name()]) )
unset( $_COOKIE[session_name()] );

but the problem is the same:
The problem is that when I go back to my homepage (using the same browser)
the shopping from the previous session is still in the cart.

I've tried placing phpinfo(); after the code above, and each time it tells
me that for HTTP_COOKIE, PHPSESSID=7cdb552e41b9ba6d293ffcead527530f (or
whatever my session was.)

ie. PHPSESSID still exists after the session has been destroyed using
session_destroy().

Is the PHPSESSID cookie the problem here? ie. the current session is being
destroyed, but when I use session_start() at the top of the next page, is
the previous session recalled using the PHPSESSID cookie?

I'd be very grateful if someone can offer a solution to this problem,
please. I've been trying to solve this for several hours and would
appreciate your help. Thanks in advance!