Prior work has shown that the sensitivity of a tumour to a specific drug can be predicted from a molecular signature of gene expressions. This is an important finding for improving drug efficacy and personalizing drug use. In this paper, we present an analysis strategy that, compared to prior work, maintains more information and leads to improved chemosensitivity prediction. Specifically we show (a) that prediction is improved when the GI50 value of a drug is estimated by all available measurements and fitting a sigmoid curve and (b) application of regression techniques often results in more accurate models compared to classification techniques. In addition, we show that (c) modern variable selection techniques, such as MMPC result in better predictive performance than simple univariate filtering. We demonstrate the strategy on 59 tumor cell lines after treatment with 118 fully characterized drugs obtained by the National Cancer Institute (NCI 60 screening) and biologically comment on the identified molecular signatures of the best predicted drugs.