Searching for sources of inspiration is central to creative design; however, we have limited knowledge of individual inspiration search strategies in response to varying levels of task constraints. We studied 39 high-school students' inspiration search strategies using Google Images. Low task constrainedness led to "divergent search" marked by quick iterations, limited design task usage, and a heterogeneous image set. Intermediate constrainedness prompted "in-depth," "on-task exploration" characterized by slow and careful iterations with more search result examination, extensive design task usage, and homogenous images. High constrainedness led to "flexible bracketing" with quick, flexible design task use, ending with heterogeneous images. Images from the intermediately and highly constrained conditions generated more ideas and were perceived as more inspiring (relative to low) in a new group of students. We discuss the idea of a 'sweet spot' of constrainedness in an inspiration search process in design and consider implications for design research and future work.