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Automatic Speech Recognition systems integrate three main knowledge sources: acoustic models, pronunciation dictionary and language models. In contrast to common practices, where each source is optimized independently, then combined in a finite-state search space, we investigate here a training procedure which attempts to adjust (some of) the parameters after, rather than before, combination. To this end, we adapted a discriminative training procedure originally devised for language models to the more general case of arbitrary finite-state graphs. Preliminary experiments performed on a simple name recognition task demonstrate the potential of this approach and suggest possible improvements.