Dynamic shim updating (DSU) of the zero- to second-order spherical harmonic field terms has previously been shown to improve the magnetic field homogeneity in the human brain at 4 Tesla. The increased magnetic field inhomogeneity at 7 Tesla can benefit from inclusion of third-order shims during DSU. However, pulsed higher-order shims can generate a multitude of temporally varying magnetic fields arising from eddy-currents that can strongly degrade the magnetic field homogeneity.The first realization of zero- to third-order DSU with full preemphasis and B(0) compensation enabled improved shimming of the human brain at 7 Tesla not only in comparison with global (i.e. static) shimming, but also when compared to state-of-the-art zero- to second-order DSU. Temporal shim-to-shim interactions were measured for each of the 16 zero- to third-order shim coils along 1D column projections on a spherical phantom. The decomposition into up to 3 exponentials allowed full preemphasis and B(0) compensation of all 16 shims covering 67 potential shim-to-shim interactions. Despite the significant improvements achievable with DSU, the magnetic field homogeneity is still not perfect even when updating all zero- through third-order shims. This is because DSU is still inherently limited by the shallowness of the low order spherical harmonic fields and their inability to compensate the higher-order inhomogeneities encountered in vivo. However, DSU maximizes the usefulness of conventional shim coil systems and provides magnetic field homogeneity that is adequate for a wide range of applications.