  We address the physical mechanism responsible for the emergence of
magnetization plateaux in the Shastry-Sutherland model. By using a hierarchical
mean-field approach we demonstrate that a plateau is stabilized in a certain
{\it spin pattern}, satisfying {\it local} commensurability conditions derived
from our formalism. Our results provide evidence in favor of a robust local
physics nature of the plateaux states, and are in agreement with recent NMR
experiments on $\scbo$.
