The remainder of this report is organized as follows. Part 1 presents and illustrates a set of analysis tools that meet the goals outlined above. These methods include the use of small exponential basis sets and transformed versions of those basis sets to efficiently capture and record the information available from the data. A practical definition of resolution is offered based on the geometric interval needed to generate basis sets that fit the data adequately. Autoregressive methods, in particular the Matrix Pencil Method, are then used. The resulting parameters are subjected least-squares refinement and to uncertainty analysis using the Fisher Information Matrix and using Monte Carlo explorations of likely parameter values. Average relaxation rates and average relaxation times are then introduced as parameters that partially but usefully describe the effective width of distributions of relaxation rates underlying the measured decay curves. An approach to regularization based on viewing the relaxation rate distributions in a Fourier domain is presented. Unlike other regularization methods, this endows widths of peaks in quasi-continuous renderings with definite and recognizable physical meaning. The last section of Part 1 generalizes the methods to two-dimensional data sets. Part 2 of the report provides deeper conceptual and mathematical descriptions of some underpinnings of the methods. The discussion in Part 2 is organized around the concept of sloppy models and Fisher Information.