We present new dedicated core surface field models spanning the decade from 2000.0 to 2010.0. These models, called gufm‐sat, are based on CHAMP, Ørsted and SAC‐C satellite observations along with annual differences of processed observatory monthly means. A spatial parametrization of spherical harmonics up to degree and order 24 and a temporal parametrization of sixth‐order B‐splines with 0.25 yr knot spacing is employed. Models were constructed by minimizing an absolute deviation measure of misfit along with measures of spatial and temporal complexity at the core surface. We investigate traditional quadratic or maximum entropy regularization in space, and second or third time derivative regularization in time. Entropy regularization allows the construction of models with approximately constant spectral slope at the core surface, avoiding both the divergence characteristic of the crustal field and the unrealistic rapid decay typical of quadratic regularization at degrees above 12. We describe in detail aspects of the models that are relevant to core dynamics. Secular variation and secular acceleration are found to be of lower amplitude under the Pacific hemisphere where the core field is weaker. Rapid field evolution is observed under the eastern Indian Ocean associated with the growth and drift of an intense low latitude flux patch. We also find that the present axial dipole decay arises from a combination of subtle changes in the southern hemisphere field morphology.