Before revision:  We introduce a method of simplification for emanation graphs of grade k= 2 , which makes it a competent spanner for many possible use cases such as network visualizationand geometric routing. In particular, the simplification reduces the number of Steiner points by half and also significantly decreases the total)\approx 3.41.
After revision:  We introduce a method of simplification for emanation graphs of grade k= 2 +\sqrt{2)\approx 3.41.