Energy funneling is a phenomenon that has been exploited in optoelectronic devices based on low-dimensional materials to improve their performance. Here, we introduce a new class of two-dimensional semiconductor, characterized by multiple regions of varying thickness in a single confined nanostructure with homogeneous composition. This "noninteger 2D semiconductor" was prepared via the structural transformation of two-octahedron-layer-thick (n = 2) 2D cesium lead bromide perovskite nanosheets; it consisted of a central n = 2 region surrounded by edge-lying n = 3 regions, as imaged by electron microscopy. Thicker noninteger 2D CsPbBr₃ nanostructures were obtained as well. These noninteger 2D perovskites formed a laterally coupled quantum well band alignment with virtually no strain at the interface and no dielectric barrier, across which unprecedented intramaterial funneling of the photoexcitation energy was observed from the thin to the thick regions using time-resolved absorption and photoluminescence spectroscopy.