  This paper gives a precise structure theorem for the class of graphs which do
not contain $W_4$ as an immersion. This strengthens a previous result of
Belmonte at al. that gives a rough description of this class. In fact, we prove
a stronger theorem concerning rooted immersions of $W_4$ where one terminal is
specified in advance. This stronger result is key in a forthcoming structure
theorem for graphs with no $K_{3,3}$ immersion.
