Layout synthesis refers to the problem of arranging objects subject to design preferences and structural constraints. Applications include furniture arrangement, space partitioning (e.g. subdividing a house into rooms), urban planning, and other design tasks. Computeraided support systems are essential tools for architects and designers to produce custom, functional layouts. Existing systems, however, do not learn the designer's preferences, and therefore fail to generalize across sessions or instances. We propose addressing layout synthesis by casting it as a constructive preference elicitation task. Our solution employs a coactive interaction protocol, whereby the system and the designer interact by mutually improving each other's proposals. The system iteratively recommends layouts to the user, and learns the user's preferences by observing her improvements to the recommendations. We apply our system to two design tasks, furniture arrangement and space partitioning, and report promising quantitative and qualitative results on both.