Organizations have recently begun to deploy conversational task assistants that collaborate with business users to partially automate their work tasks. These assistants are becoming more intelligent: users initiate automated task support through natural language, and the system can dynamically orchestrate new task sequences accordingly. As these tools become more intelligent and automated, they sometimes shift control away from users to increase process efficiency at the cost of consequences for users’ preferences and productivity. Particularly in high stakes work environments, this shift raises questions of when automation is suitable and how to delegate agency such that users feel sufficiently in control of their tasks. We explored these questions through two studies comprised of interviews and co-design activities with business users and identified four task dimensions along which their automation and interaction preferences vary: process consequence, social consequence, task familiarity, and task complexity. These dimensions are useful for understanding when, why, and how to delegate control between users and conversational task assistants.