The last approach with my team was the Agile stand-up meeting. I felt these meetings were straight to the points when a team member brief other colleagues on his progress in brief and what is his plan for that day/s to come and what are the impediments that requires the team support or mine. I felt that controlling the inputs was easier and through time the team got used to the style and it became a faster process for daily stand-ups.
As for influencing , I definitely advise members to discuss the items as per the meeting Agenda and If an issue develops to become a snowball I would ask them to take note of it and schedule a different session to align and agree on a solution.