The combination of Automatic Speech Recognition (ASR) systems generally relies on a posteriori merge of system outputs or on a cross-adaptation. In this paper, we propose an integrated approach where the search of a primary system is driven by the outputs of a secondary one. This method allows to drive the primary system search by using the one-best hypotheses and the word posteriors gathered from the secondary system. Experiments are carried out within the experimental framework of the ESTER evaluation campaign [1]. Results show that the driven decoding algorithm significantly outper-forms the two single ASR systems (-8% of relative WER,-1.7% absolute). Finally, we investigate the interactions between driven decoding and cross-adaptations. The best cross-adaptation strategy in combination with the driven decoding process brings to a final absolute gain of about 1.9% WER.