  In this article we consider large data Wave-Maps from $\mathbb{R}^{2+1}$ into
a compact Riemannian manifold $(\mathcal{M},g)$, and we prove that regularity
and dispersive bounds persist as long as a certain type of bulk
(non-dispersive) concentration is absent. In a companion article we use these
results in order to establish a full regularity theory for large data
Wave-Maps.
