An inversion recovery (IR) bSSFP measurement allows to calculate quantitative parameter maps assuming mono-exponential signals. However, the measured signals often show multi-exponential behavior due to partial volume effects or tissue microstructure. With IR bSSFP it is possible to extract a spectrum of the apparent relaxation times T1* and hence to identify multiple components in each voxel. By integration over specific T1* ranges, different brain-components like white matter, gray matter or CSF can be mapped. In this work, we demonstrate that even short-living components such as myelin water are detected providing helpful information for diagnostic purposes, e.g. in neurodegenerative diseases.