  Using infinite projected entangled-pair states (iPEPS), we show that the
Shastry-Sutherland model in an external magnetic field has low-magnetization
plateaus which, in contrast to previous predictions, correspond to crystals of
bound states of triplets, and {\it not} to crystals of triplets. The first
sizable plateaus appear at magnetization 1/8, 2/15 and 1/6, in agreement with
experiments on the orthogonal-dimer antiferromagnet SrCu$_2$(BO$_3$)$_2$, and
they can be naturally understood as regular patterns of bound states, including
the intriguing 2/15 one. We also show that, even in a confined geometry, two
triplets bind into a {\it localized} bound state with $S_z=2$. Finally, we
discuss the role of competing domain-wall and supersolid phases as well as that
of additional anisotropic interactions.
