  In this paper we build an explicit example of a minimal bubble on a Willmore
surface, showing there cannot be compactness for Willmore immersions of
Willmore energy above $16 \pi$. Additionnally we prove an inequality on the
second residue for limits sequences of Willmore immersions with simple minimal
bubbles. Doing so, we exclude some gluing configurations and prove compactness
for immersed Willmore tori of energy below $12 \pi$.
