Login issues with multiple sites in the same domain (session cookie collision) in drupal 7 (7.19)

Hi,
my problem is very similar to http://drupal.org/node/56357
just a new version of drupal.
I have several different sites under one domain behind a proxy:
example.com/site1 ($base_url = 'example.com/site1' ; cookie_domain='example.com')
example.com/site2 ($base_url = 'example.com/site2' ; cookie_domain='example.com')
example.com/site3 ($base_url = 'example.com/site3' ; cookie_domain='example.com')
login into one site logs me out of the others.
I know cookie domain is supposed to do this, however when I omit it I can't login (I think due to the '/' in base_url)
can anyone tell me how to change session name to be unique / how to solve this issue ?