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CBR systems that are built for the classification problems are called CBR classifiers. This paper presents a novel and fast approach to building efficient and competent CBR classifiers that combines both feature reduction (FR) and case selection (CS). It has three central contributions: 1) it develops a fast rough-set method based on relative attribute dependency among features to compute the approximate reduct, 2) it constructs and compares different case selection methods based on the similarity measure and the concepts of case coverage and case reachability, and 3) CBR classifiers built using a combination of the FR and CS processes can reduce the training burden as well as the need to acquire domain knowledge. The overall experimental results demonstrating on four real-life data sets show that the combined FR and CS method can preserve, and may also improve, the solution accuracy while at the same time substantially reducing the storage space. The case retrieval time is also greatly reduced because the use of CBR classifier contains a smaller amount of cases with fewer features. The developed FR and CS combination method is also compared with the kernel PCA and SVMs techniques. Their storage requirement, classification accuracy, and classification speed are presented and discussed.