A magnetic resonance system has a basic magnet system that generates a temporally static, spatially homogeneous basic magnetic field in an examination volume of the magnetic resonance system, and a radio-frequency system. An overlay system generates overlay fields in the examination volume that, together with the basic field, form a complete field. The overlay system has at least one first order field system and at least one second order field system. The first order field system generates fields that, to a first approximation, exhibit a spatial dependency of the first order. The second order field system generates fields that, to a first approximation, exhibit a spatial dependency of the second order. A control device operates the radio-frequency system with an operating frequency and controls the first and second order field systems to cause a deviation between the complete field and a desired gradient to exhibit a spatial dependency of the second order and to satisfy a minimum condition within a correction volume.