In real world applications of supervised learning methods, training and test sets are often sampled from the distinct distributions and we must resort to domain adaptation techniques. One special class of techniques is Covariate Shift Adaptation, which allows practitioners to obtain good generalization performance in the distribution of interest when domains differ only by the marginal distribution of features. Traditionally, Covariate Shift Adaptation is implemented using Importance Weighting which may fail in high-dimensional settings due to small Effective Sample Sizes (ESS). In this paper, we propose (i) a connection between ESS, high-dimensional settings and generalization bounds and (ii) a simple, general and theoretically sound approach to combine feature selection and Covariate Shift Adaptation. The new approach yields good performance with improved ESS.