Covariate shift is a specific class of selection bias that arises when the marginal distributions of the input features X are different in the source and the target domains while the conditional distributions of the target Y given X are the same. A common technique to deal with this problem, called importance weighting, amounts to reweighting the training instances in order to make them resemble the test distribution. However this usually comes at the expense of a reduction of the effective sample size. In this paper, we show analytically that, while the unweighted model is globally more biased than the weighted one, it may locally be less biased on low importance instances. In view of this result, we then discuss a manner to optimally combine the weighted and the unweighted models in order to improve the predictive performance in the target domain. We conduct a series of experiments on synthetic and real-world data to demonstrate the efficiency of this approach.