Creating Minimum Spanning Tree based on street network using ArcGIS Desktop?

I am using ArcGIS Desktop 10.0 SP2 (ArcView License) and Network Analyst.

Background: I try to create a network of fiber optic cables to specific points along a street network.

Here is what I want to do: I want to create a Minimum Spanning Tree based on a street network to give me the shortest path between a couple of fiber optic access points. The MST should start at a fiber optic distribution point and "span out" to the access points.

What I tried so far: I tried to manage it with the Network Analyst and the 'Closest Facility' analysis. The problem is that it handles each connection between a distribution point and a access point as a independent solution (end up in a single route) - so its not the MST. I am not sure if something like that is possible with a geometric network (with sinks and sources) and a flow direction.