Show only sites where user is administrator in 'My Sites'

Is it possible to change the ‘My Sites’ menu in Multisite, so that it only shows sites where the user is administrator?

The way mine is set up, all users become a member of every site, and there is no access to the admin for anybody other than the administrator, so I can see this menu filling quickly and getting confusing for the user, not seeing exactly where just their sites are.

Thanks.