  Using density-functional theory (DFT) band-structure calculations, we study
the crystal structure, the lattice dynamics, and the magnetic interactions in
the Shastry-Sutherland magnet SrCu$_2$(BO$_3$)$_2$ under pressure,
concentrating on experimentally relevant pressures up to 4 GPa. All tendencies
inside the candidate intermediate phases are thoroughly worked out, including
specific predictions for some Raman active phonon modes that could be used to
pin down the nature of the intermediate phase.
