How do you best re-structure a team?

First of all you need to identify why there is a need for a restructure.  Is it financial, is it because the business needs have changed, i.e. working differently or if the organisation as a whole has changed, i.e. merger.  It could also be because the feedback about the department mean it does not work as well as it could, is this to do with business process or disengagement of staff.

You then need to identify what the department requirements are, what areas does it need to cover, maybe also revisit numbers, for example, when dealing with invoice transactions, is the number still the same, have the increased/decreased.  Are the transactions to be managed a different way where manual intervention is reduced.

Without stakeholder engagement a restructure would not work as well.  Get buy in from users, internal and external, maybe find out how they find the service. 

Involve the existing team in discussions, they may not like the fact that its changing, but including them ensures an open and transparent process.  Get on board their ideas, they may be able to give some good insight into how to do it better.

Consult on a restructure, get feedback and views from users, after all, without their using the service there would not be a need for the department at all.

Give clear timelines on when its expected to be introduced, this way there is a clear end goal to meet.  Set the goal and work back on dates for consultant, management review and implementation.

These steps would cover why, how, when and who should be involved in a restructure.