  The interplay between magnetism and superconductivity in LaFeAsO_0.945F_0.055
was studied as a function of hydrostatic pressure up to p~2.4GPa by means of
muon-spin rotation (\muSR) and magnetization measurements. The application of
pressure leads to a substantial decrease of the magnetic ordering temperature
T_N and a reduction of the magnetic phase volume and, at the same time, to a
strong increase of the superconducting transition temperature T_c and the
diamagnetic susceptibility. From the volume sensitive \muSR measurements it can
be concluded that the superconducting and the magnetic areas which coexist in
the same sample are inclined towards spatial separation and compete for phase
volume as a function of pressure.
