Syntax-guided synthesis searches for an implementation of a given specification by exploring large spaces of candidate programs. Sketches reduce these search spaces, making synthesis more tractable, by predefining the structure of the desired implementation. Typically, this structure is obtained through human insight—this paper introduces a method for interactive, tool-supported discovery of such structure. The key idea is to decompose the specification into subcomputations such that the decomposition dictates the sketch. We rely on a readily obtainable specification that is nothing more than a finite set of sample input-output pairs or execution traces of the desired program. We introduce two complementary decomposition operators and demonstrate them on case studies. We find that interactive structure discovery extends the reach of computer-aided programming to problems that cannot be solved with synthesis alone.