1. A method for acquiring a magnetic resonance data set of a plurality of slices of a volume of interest in an examination subject, comprising: obtaining a plurality of trigger signals from an examination subject situated in a magnetic resonance data acquisition unit based on respiration of said examination subject; providing said trigger signals to a control computer and, upon receipt of each trigger signal, beginning, from said control computer, operation of said magnetic resonance data acquisition unit to execute a respective fat saturation magnetic resonance data acquisition procedure comprising an acquisition block having a plurality of echo trains respectively relating to different individual slices of a plurality of slices of a volume of interest in the examination subject; from said control computer, operating said magnetic resonance data acquisition unit to acquire, from said echo trains in each respective acquisition block, magnetic resonance data for each of said plurality of individual different slices and entering the magnetic resonance data acquired for each individual slice into a respective portion of k-space in an electronic memory organized as k-space; from said control computer, in at least two of said acquisition blocks, operating said magnetic resonance data acquisition unit to acquire the magnetic resonance data from said plurality of individual different slices in respective sequential orders of said slices that differ from each other; in an image reconstruction computer having access to said electronic memory, reconstructing a magnetic resonance image of each slice from the magnetic resonance data entered, in all of said acquisition blocks, into the respective portion of k-space for that slice; and from said image reconstruction computer, making the respective reconstructed images of the plurality of slices available in electronic form as at least one data file.