Change vertex order

[ChrisMathers]

I would like to be able to change the order of the vertexes of a polygon. I often find myself wanting to edit a polygon using the sketch tool but needing to edit from a segment that is not at the end of the initial digitizing. This could also simply be the ability to insert vertices via sketch instead of with the edit tool. By selecting a line segment and the appropriate function from the drop down you could begin sketching and the new vertices would be inserted along the new line.

[StephenRhone1]

Perhaps they wouldn't even need to change the order of vertices to do this -- if we could right-click any vertex and tell ArcMap that we wanted this vertex to be our starting point for using sketch and edit tools, that would be just as good.  It would be just like inserting new vertices between two existing ones, as you said.