The problem of learning fuzzy rule-bases is analyzed from the perspective of finding a favorable balance between the accuracy of the system, the speed required to learn the rules, and finally, the interpretability of the rule-bases obtained. Therefore, we introduce a complete design procedure to learn and then optimize the system rule-base, called the Precise and Fast Fuzzy Modeling approach. Under this paradigm, fuzzy rules are generated from numerical data using a parameterizable greedy-based learning method called Selection-Reduction, whose accuracy-speed efficiency is confirmed through empirical results and comparisons with reference methods. Qualitative justification for this method is provided based on the co-action between fuzzy logic and the intrinsic properties of greedy algorithms. To complete the Precise and Fast Fuzzy Modeling strategy, we finally present a rule-base optimization technique driven by a novel rule redundancy index which takes into account the concepts of distance between rules and the influence of a rule over the dataset. Experimental results show that the proposed index can be used to obtain compact rule-bases which remain very accurate, thus increasing system interpretability.