Signal formation in a photon-counting x-ray/gamma-ray imaging detector is a complex process resulting in detector signals governed by multiple random effects. Recovering maximum possible information about event attributes of interest requires a systematic collection of calibration data and analysis provided by estimation theory. In this context, a likelihood model provides a description of the connection between the observed signals and the event attributes. A quantitative measure of how well the measured signals can be used to produce an estimate of the parameters is given by Fisher Information analysis. In this work, we demonstrate several applications of the Fisher Information Matrix (FIM) as a powerful and practical tool for investigating and optimizing potential next-generation x-ray/gamma-ray detector designs, with an emphasis on medical-imaging applications. Using FIM as a design tool means to explore the physical detector design choices that have a relationship with the FIM through the likelihood function, how are they interrelated, and determining whether it is possible to modify any of these choices to yield or retain higher values for Fisher Information. We begin by testing these ideas by investigating a new type of a semiconductor detector, a Cadmium Telluride (CdTe) detector with double-sided-strip geometry developed by our collaborators at the Japan Aerospace Exploration Agency (JAXA). The statistical properties of the detector signals as a function of interaction positions in 3D (x, y, z) are presented with mathematical expressions as well as experimental data from measurements using synchrotron radiation at the Advanced Photon Source at Argonne National Laboratory. We show the computation of FIM for evaluating positioning performance and discuss how various detector parameters, that are identified to affect FIM, can be used in detector optimization. Next, we show the application of FIM analysis in a detector system based on multi-anode photomultiplier tubes coupled to a monolithic scintillator in the design of smart electronic read-out strategies. We conclude by arguing that a detector system is expected to perform the best when the hardware is optimized jointly with the estimation algorithm (simply referred to as the "software" in this context) that will be used with it. The results of this work lead to the idea of a detector development approach where the detector hardware platform is developed concurrently with the software and firmware in order to achieve optimal performance.