This paper discusses phonetic accommodation of 20 native German speakers interacting with the simulated spoken dialogue system Mirabella in a Wizard-of-Oz experiment. The study examines intonation of wh-questions and pronunciation of allophonic contrasts in German. In a question-and-answer exchange with the system, the users produce predominantly falling intonation patterns for wh-questions when the system does so as well. The number of rising patterns on the part of the users increases significantly when Mirabella produces questions with rising intonation. In a map task, Mirabella provides information about hidden items while producing variants of two allophonic contrasts which are dispreferred by the users. For the [ɪç] vs. [ɪk] contrast in the suffix ⟨-ig⟩, the number of dispreferred variants on the part of the users increases significantly during the map task. For the [εː] vs. [eː] contrast as a realization of stressed ⟨-ä-⟩, such a convergence effect is not found on the group level, yet still occurs for some individual users. Almost every user converges to the system to a substantial degree for a subset of the examined features, but we also find maintenance of preferred variants and even occasional divergence. This individual variation is in line with previous findings in accommodation research.