  An increasing number of measurements in fundamental and applied physics rely
on magnetically shielded environments with sub nano-Tesla residual magnetic
fields. State of the art magnetically shielded rooms (MSRs) consist of up to
seven layers of high permeability materials in combination with highly
conductive shields. Proper magnetic equilibration is crucial to obtain such low
magnetic fields with small gradients in any MSR. Here we report on a scheme to
magnetically equilibrate MSRs with a 10 times reduced duration of the magnetic
equilibration sequence and a significantly lower magnetic field with improved
homogeneity. For the search of the neutron's electric dipole moment, our
finding corresponds to a linear improvement in the systematic reach and a 40 %
improvement of the statistical reach of the measurement. However, this
versatile procedure can improve the performance of any MSR for any application.
