1. A method for operating a magnetic resonance (MR) apparatus, comprising: operating an MR apparatus, in which a subject is situated, to acquire MR data from the subject; providing the acquired MR data to a computer and, in said computer, generating a plurality of quantitative parameter maps each representing multiple parameters having an effect on said MR data, by generating each quantitative parameter map by applying a tentative signal model to the MR data; in said computer, for each tentative signal model, performing an initial analysis to determine whether any of said parameters can be set to at least a locally constant value and, if so, setting respective parameters to respective locally constant values, thereby producing an initially analyzed tentative model; in said computer, performing at least a quality of fit analysis of the initially analyzed tentative signal model; in said computer, selecting, as a final signal model, a tentative signal model, among said plurality of tentative signal models, for which at least said quality of fit analysis is best; and generating a parameter map using said tentative signal model for which said quality of fit is best, and displaying that parameter map at a display monitor in communication with said computer.