  Using perturbative continuous unitary transformations, we determine the
long-range interactions between triplets in the Shastry-Sutherland model, and
we show that an unexpected structure develops at low magnetization with
plateaux progressively appearing at 2/9, 1/6, 1/9 and 2/15 upon increasing the
inter-dimer coupling. A critical comparison with previous approaches is
included. Implications for the compound SrCu$_2$(BO$_3$)$_2$ are also
discussed: we reproduce the magnetization profile around localized triplets
revealed by NMR, we predict the presence of a 1/6 plateau, and we suggest that
residual interactions beyond the Shastry-Sutherland model are responsible for
the other plateaux below 1/3.
