If a supervisor, another teams' manager or a different team member comes to my desk/area and asks questions or wants to discuss an issue, some of my more enthusiastic team members jump in and start going into useless details, talking about minor issues and sometimes also alarming external people about things that only my team should worry about.
I have always encouraged and supported an open communication, feedback-oriented and participative culture within my team, but this may not work when it comes to other teams or managers in the company, as there are so many conflicting interests and "agendas" I need to deal with.
For example, I may want to keep a discussion short and simple, just to be able to carry on with our teams' work. Instead my subordinates will get into the discussion and auto-commit themselves to new tasks.
Another example is that I am trying to negotiate some help or approval by another team manager or my own supervisor, but to do that I need to present the information in a very specific order and way. If my subordinates come and share the whole discussion, that will be difficult to achieve.
What can I do to keep my team happy and participative within the team, but stay low profile externally - and most importantly, to stop interfering when I am leading a discussion?