One of the most important characteristics of Quantitative Structure Activity Relashionships (QSAR) models is their predictive power. The latter can be defined as the ability of a model to predict accurately the target property (e.g., biological activity) of compounds that were not used for model development. We suggest that this goal can be achieved by rational division of an experimental SAR dataset into the training and test set, which are used for model development and validation, respectively. Given that all compounds are represented by points in multidimensional descriptor space, we argue that training and test sets must satisfy the following criteria: (i) Representative points of the test set must be close to those of the training set; (ii) Representative points of the training set must be close to representative points of the test set; (iii) Training set must be diverse. For quantitative description of these criteria, we use molecular dataset diversity indices introduced recently (Golbraikh, A., J. Chem. Inf. Comput. Sci., 40 (2000) 414-425). For rational division of a dataset into the training and test sets, we use three closely related sphere-exclusion algorithms. Using several experimental datasets, we demonstrate that QSAR models built and validated with our approach have statistically better predictive power than models generated with either random or activity ranking based selection of the training and test sets. We suggest that rational approaches to the selection of training and test sets based on diversity principles should be used routinely in all QSAR modeling research.