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Congratulations! Amazing work, and I love the video - is that all just a screencapture?
Can I also make a plug for a project I'm working on? It's called Redline (www.redline.cc), and it allows anyone on your team to make markups on the site and have it auto-generate bugs in your Project Management workflow (Basecamp, Pivotal, etc.) Feel free to message me about what you think as we're still in beta.
I think it all depends on what you're doing.
Most Program Managers I know (both at consultancies and in-house) love Basecamp. They have all their contacts (dev, design, stakeholders) easily accessible. You can message, have conversations, create a schedule, upload files. It tends to allow for long conversations - oftentimes I can just go to that thread and check up on the status of a feature. Other tools I've heard that are vying for the same space are Insightly, Liquid Planner.
If you're doing more granular development - like it's pretty clear what you have to build, then most everyone I know likes Pivotal Tracker best. It's quick to add a ton of "stories" or tasks, and then drag and re-order them depending on the priority. You can distinguish between a Backlog queue (stuff to be done in certain sprints) versus an Icebox queue (what you really want, but honestly everyone agrees can't be done for V.1. But nobody wants to forget that we've thought of it!). As a designer, you can attach files to a story if the developer sez "I need these assets to finish this feature off".
Trello is supposed to be a much more intuitive approach to the same idea.
Sorry for the long post, just thought it's a great topic I've been thinking about myself!
Be nice. Or else.
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