Re-organizing your team structure only makes sense as part of a larger effort at process improvement. Most organizations build functional silos - nothing wrong with that, and lots of very good reasons to do so. Then there are the processes that focus on your customers, and these generally move through your functions.
Now here's the thing: re-organizing your functions only moves the employees who are doing the process work from one silo to another. Re-organization does not change the flow of the process to the customer. Thus, if your goal is to reduce complexity, then a process-focused approach is much more likely to result in increased efficiency as well as effectiveness.
The process analysis techniques are standard; and yes, they are part of the set of tools and techniques of Lean and Six Sigma. But don't be biased against the tools for that reason. They are good, solid techniques -- Value Stream mapping, functional deployment charts, and the like -- and they generally create some significant "ah-ha's" among the people involved in the process when they understand the waste and unneeded complexity of a process that may have made good sense when it was first designed. Frequently this leads to waste removal (stopping the unneeded tasks); and sometimes indicates the need to make modification to the functional silos (re-organizing). Together, it's a powerful combination.
