We present a strategy for increasing the anatomical realism of organoids by applying asymmetric cues to mimic spatial information that is present in natural embryonic development, and demonstrate it using mouse kidney organoids. Existing methods for making kidney organoids in mice yield developing nephrons arranged around a symmetrical collecting duct tree that has no ureter. We use transplant experiments to demonstrate plasticity in the fate choice between collecting duct and ureter, and show that an environment rich in BMP4 promotes differentiation of early collecting ducts into uroplakin-positive, unbranched, ureter-like epithelial tubules. Further, we show that application of BMP4-releasing beads in one place in an organoid can break the symmetry of the system, causing a nearby collecting duct to develop into a uroplakin-positive, broad, unbranched, ureter-like 'trunk' from one end of which true collecting duct branches radiate and induce nephron development in an arrangement similar to natural kidneys. The idea of using local symmetry-breaking cues to improve the realism of organoids may have applications to organoid systems other than the kidney.