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Have a look at Gemini. The guys at Countersoft have gone all out with the latest version and I can highly recommend it. It's free for up to 3 users and has a comprehensive REST api you can interface with. It's also highly flexible and configurable so you can structure your projects easily to include only the stuff that's relevant to your project(s).

You might want to look at: getsatisfaction.com - has SSO (called Fastpass) and APIs Atlassian JIRA - has SSO through Atlassian's Crowd product, and various other options, plus APIs getsatisfaction is quite end-user oriented, while JIRA is more of a developer's bug tracker.

You might want to consider Basecamp. I can only post two links since I am a new user, but here is a link for all the reasons you should try Basecamp. It contains all the features you requested above. Seems to be the right direction for your needs.