For reduction of artifacts when acquiring magnetic resonance (MR) data using an MR apparatus, a SPAR pulse, which acts on spins in a first predetermined frequency range, and a saturation pulse, which acts on spins in a second predetermined frequency range, are radiated. A gradient for spatial encoding is activated at the same time as the saturation pulse, so that the saturation pulse acts on an edge region adjacent to the volume segment. The edge region borders an ellipsoidal useful volume of the scanner of the MR apparatus, in which the strength of the B0 field changes in terms of magnitude by no more than 30 ppm. Spoiler gradients are activated to destroy a transverse magnetization, before an RF excitation pulse, adjusted to the SPAIR pulse, is radiated. MR data are acquired after the SPAIR pulse, the saturation pulse and the RF excitation pulse. The second frequency range is adjusted to the first frequency range.