Most side-channel attacks that have been published in the open literature assume known- or chosen-message adversarial scenarios. In this paper, we analyze the increase of the attacks’ efficiencies that can be obtained by adaptively selecting the messages. For this purpose, we first describe a generic strategy that allows an adversary to take advantage of this capability. We show that it can be applied to any differential power or electromagnetic analysis attack, against unprotected or protected devices and exploiting profiled or non-profiled leakage models. Then, we provide various experiments to quantify these improvements. Finally, we discuss the optimality of our strategy and its implications for the security evaluation of leakage-resilient cryptographic hardware.