Designing interactions for human-AI teams (HATs) can be challenging due to an AI agent’s potential autonomy. Previous work suggests that higher autonomy does not always improve team performance, and situation-dependent autonomy adaptation might be beneficial. However, there is a lack of systematic empirical evaluations of such autonomy adaptation in human-AI interaction. Therefore, we propose a cooperative task in a simulated shared workspace to investigate effects of fixed levels of AI autonomy and situation-dependent autonomy adaptation on team performance and user satisfaction. We derive adaptation rules for AI autonomy from previous work and a pilot study. We implement these rule for our main experiment and find that team performance was best when humans collaborated with an agent adjusting its autonomy based on the situation. Additionally, users rated this agent highest in terms of perceived intelligence. From these results, we discuss the influence of varying autonomy degrees on HATs in shared workspaces.