This chapter presents problem decomposition as a practical method for reframing complex, hybrid problems into manageable subcomponents that better align human and AI strengths. It explains that decomposition is not about oversimplifying complexity but about gaining traction on it, thus making problem structure visible while preserving interconnections. The chapter introduces Zoom Cycling, the disciplined skill of moving between detailed and holistic perspectives to ensure clarity without losing context. Through examples such as a national mental health crisis and a multinational firm’s cyberattack response, it shows how decomposing a single overwhelming challenge into sub-hybrid problems enables targeted collaboration strategies (e.g., Automated Execution, Machine-Augmented Decision-Making, Expert Judgment). Four types of decomposition—functional, temporal, spatial, and thematic—are detailed alongside their strategic purposes: clarity, resource targeting, reframing focus, progress acceleration, complexity management, and responsibility allocation. The chapter also cautions against flawed or excessive decomposition, illustrating lessons from “New Coke,” the Iraq WMD assessment, and the opioid crisis. Ultimately, decomposition emerges as a living strategy that adapts to problem movement, enhances contextual fit, and strengthens human-AI collaboration by ensuring the right cognitive and computational resources are applied to the right parts of a problem at the right time.