People turn to generative artificial intelligence (AI) to make ideation less effortful. Turning a vague idea into a mature concept is hard work, and offloading it to AI is tempting. However, our research shows that this strategy can backfire; the lower-effort form of AI support often produced less creative ideas. In an online experiment, 276 people refined ideas for an innovation challenge working alone or with AI-generated text or images. Image-based generative AI had a double-edged effect; it significantly reduced effort compared with working alone or using text-based support. However, ideas from image-based support were also 18% less creative than those from the more effortful text-based support. The reason lies in what each format leaves for the human to do. Images specify all details of an idea, leaving less creative room for humans, but text leaves gaps that humans can complete with their imagination—a process that is effortful yet stimulates creativity. Crucially, the effect also depends on how far the idea is developed. Text-based input helps most when the idea is already well developed because humans can then make the most of it. The major takeaway is do not use AI just to save effort but use it where the effort pays off.