1. A method for operating a magnetic resonance (MR) apparatus, comprising: operating the MR apparatus, a subject is situated therein, 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, each quantitative parameter map being generated by applying a respective tentative signal model, from a plurality of signal models, 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, so as to produce an initially analyzed tentative model from each tentative signal model, and thereby producing a plurality of initially analyzed tentative signal models; in said computer, performing at least a quality of fit analysis of each 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 said quality of fit analysis, for the initially analyzed tentative fit model produced therefrom, 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.