  Building on the growing evidence based on NMR, magnetization, neutron
scattering, ESR, and specific heat that, under pressure, SrCu$_2$(BO$_3$)$_2$
has an intermediate phase between the dimer and the N\'eel phase, we study the
competition between two candidate phases in the context of a minimal model that
includes two types of intra- and inter-dimer interactions without enlarging the
unit cell. We show that the empty plaquette phase of the Shastry-Sutherland
model is quickly replaced by a quasi-1D full plaquette phase when intra- and/or
inter-dimer couplings take different values, and that this full plaquette phase
is in much better agreement with available experimental data than the empty
plaquette one.
