In a method and apparatus for acquiring magnetic resonance (MR) data from a predetermined volume within an examination object, a control protocol for a gradient echo sequence is selected that specifies that gradient moments produced in said gradient echo sequence be balanced along all three spatial directions. In this gradient echo sequence a slice selection gradient is activated in a slice selection direction that produces a balanced gradient moment, with simultaneous radiation of an RF pulse that simultaneously excites nuclear spins in multiple slices of the examination object, with said excitation being repeated according to a repetition time. A phase of MR signals to be acquired from a same one of said multiple layers is varied from repetition time-to-repetition time. An additional gradient is activated in the slice selection gradient that produces an additional gradient moment that is constant over consecutive repetition times and thus overrides the condition of the gradient moments of the gradient echo sequence being balanced along said slice selection direction. The MR signals are acquired during activation of a readout gradient.