Recommendations for php email list managers?

Hi, I'm trying to set up a list manager on a hosted site. PHPlist (phplist.com) seemed promising but I read on their forums that it takes some users hours and hours to send a couple thousand emails. Without terminal access, I suspect the PHP sending page will time out long before most of my emails have been sent. Does anyone have suggestions for a quicker mailer? I'd like to be able to import users in bulk, and I'd like to let users sign up and unsubscribe automatically. PHPlist does all that but... I don't want to set it all up and then find out I can't send my newsletter. It's supposed to be an announcement-only list, BTW. /Mattias