While in Basecamp classic you were able to mark todo-lists or messages as private (only visible by your company), it seems that there's no such feature in the "all-new" version of Basecamp.
I know that you can set permissions for whole projects in way that only your company is able to access the project and that you can move whole todo-lists to another project. But that's an annoying and complicated workflow.
Is there another easy workflow which simulates the Private Items feature from Basecamp classic?
Best Answer
You're in good company - a lot of people miss the Private facilities (nice write-up here).
In one of 37Signal's early communications during the release of the new system, they stated that they are "rethinking" Private, and that they may add support for this in the future.
When you look at their "New stuff" link, you can tell that they're working hard on things - so I tend to believe that Private indeed will return (in some way) in the future.
Update!: Basecamp now supports this via Client Projects.