Session handling with cookies??

Hello, I have developed a member login system with cookies. Now I have the prob, that the session stayes existend when the browser is closed. This could couse a problem in Internet caffes for example. As second thing, I have realized, that it depends on the clients clock!! I am sending a cookie which expires in time() + $expireseconds. Unfortunatelly the time command takes the tim from the server and the cookie expires checking the client time. So... does anybody know how... 1) I get the system to delete the cookie as soon as I leave the site, or close it 2) How to work on the same time. Thanx for any help Cheers Andy